url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.index_destruct | [59, 1] | [66, 10] | rw [βpgfp.unfold] at wf | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ i = (Container.M.destruct β{ val := m, property := wf }).fst.fst | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ i = (Container.M.destruct β{ val := m, property := wfβ }).fst.fst | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ i = (Container.M.destruct β{ val := m, property := wf }).fst.fst
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.index_destruct | [59, 1] | [66, 10] | simp only [CompleteLattice.bot_sup] at wf | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ i = (Container.M.destruct β{ val := m, property := wfβ }).fst.fst | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ i = (Container.M.destruct β{ val := m, property := wfβ }).fst.fst | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ i = (Container.M.destruct β{ val := m, property := wfβ }).fst.fst
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.index_destruct | [59, 1] | [66, 10] | have β¨x, _β© := wf | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ i = (Container.M.destruct β{ val := m, property := wfβ }).fst.fst | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : (Container.M.destruct m).fst.fst = i
rightβ :
β (x : B C (Container.M.destruct m).fst.fst (Container.M.destruct m).fst.snd),
β(pgfp (WellForme... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ i = (Container.M.destruct β{ val := m, property := wfβ }).fst.fst
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.index_destruct | [59, 1] | [66, 10] | apply Eq.symm | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : (Container.M.destruct m).fst.fst = i
rightβ :
β (x : B C (Container.M.destruct m).fst.fst (Container.M.destruct m).fst.snd),
β(pgfp (WellForme... | case h
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : (Container.M.destruct m).fst.fst = i
rightβ :
β (x : B C (Container.M.destruct m).fst.fst (Container.M.destruct m).fst.snd),
β(pgfp (We... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : (Container.M.destruct m).fst.fst = i
rightβ :
β (x : B C (Container.M.destruct m).fst... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.index_destruct | [59, 1] | [66, 10] | exact x | case h
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : (Container.M.destruct m).fst.fst = i
rightβ :
β (x : B C (Container.M.destruct m).fst.fst (Container.M.destruct m).fst.snd),
β(pgfp (We... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : (Container.M.destruct m).fst.fst = i
rightβ :
β (x : B C (Container.M.destruct... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | intro β¨x, wfxβ© β¨y, wfyβ© hβ | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
β’ β (x y : M C i), R i x y β x ... | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toContainer C)... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | suffices h: x = y by
induction h
rfl | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toContainer C)... | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toContainer C)... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | apply Container.M.bisim (Ξ» x y => β i, β (wfx: WellFormed i x) (wfy:WellFormed i y), R i β¨x, wfxβ© β¨y, wfyβ©) | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toContainer C)... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toCont... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | . intro x y β¨i, wfx, wfy, rβ©
have β¨node, kβ, kβ, hβ, hβ, hββ© := hβ i β¨x, wfxβ© β¨y, wfyβ© r
let ix := (Container.M.destruct x).1.1
let nx := (Container.M.destruct x).1.2
let kx := (Container.M.destruct x).2
let iy := (Container.M.destruct y).1.1
let ny := (Container.M.destruct y).1.2
let ky := (Container.M.d... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toCont... | case a
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toConta... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exists i | case a
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toConta... | case a
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toConta... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exists wfx | case a
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toConta... | case a
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toConta... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exists wfy | case a
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toConta... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | induction h | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toContainer C)... | case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | rfl | case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toCo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | intro x y β¨i, wfx, wfy, rβ© | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
x : Container.M (toCont... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have β¨node, kβ, kβ, hβ, hβ, hββ© := hβ i β¨x, wfxβ© β¨y, wfyβ© r | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | let ix := (Container.M.destruct x).1.1 | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | let nx := (Container.M.destruct x).1.2 | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | let kx := (Container.M.destruct x).2 | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | let iy := (Container.M.destruct y).1.1 | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | let ny := (Container.M.destruct y).1.2 | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | let ky := (Container.M.destruct y).2 | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have hix := index_destruct β¨x, wfxβ© | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have hiy := index_destruct β¨y, wfyβ© | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have wfx' : β a:B C ix nx, WellFormed (C.N ix nx a) (kx a) := wf_destruct β¨x, wfxβ© | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have wfy' : β a:B C iy ny, WellFormed (C.N iy ny a) (ky a) := wf_destruct β¨y, wfyβ© | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | simp only at hix hiy wfx wfy | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exists β¨_, nodeβ© | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exists Ξ» x => (kβ x).1 | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exists Ξ» x => (kβ x).1 | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | constructor | case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toCo... | case hβ.left
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M ... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | . cases hix
have hnx: nx = node := by
apply congrArg Sigma.fst hβ
cases hnx
have hβ := Sigma.snd_equals _ _ _ hβ
rw [β hβ]
rfl | case hβ.left
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M ... | case hβ.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.left
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i n... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | . constructor
. cases hiy
have hny: ny = node := by
apply congrArg Sigma.fst hβ
cases hny
have hβ := Sigma.snd_equals _ _ _ hβ
rw [β hβ]
rfl
. intro a
exists C.N i node a
simp only [toContainer] at a
exists (by
cases hix
have : nx = node := by
apply co... | case hβ.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | cases hix | case hβ.left
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M ... | case hβ.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Containe... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.left
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i n... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have hnx: nx = node := by
apply congrArg Sigma.fst hβ | case hβ.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Containe... | case hβ.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Containe... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | cases hnx | case hβ.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Containe... | case hβ.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Con... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have hβ := Sigma.snd_equals _ _ _ hβ | case hβ.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Con... | case hβ.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Con... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | rw [β hβ] | case hβ.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Con... | case hβ.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Con... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | rfl | case hβ.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Con... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | apply congrArg Sigma.fst hβ | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toContainer C... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | constructor | case hβ.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M... | case hβ.right.left
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Contai... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | . cases hiy
have hny: ny = node := by
apply congrArg Sigma.fst hβ
cases hny
have hβ := Sigma.snd_equals _ _ _ hβ
rw [β hβ]
rfl | case hβ.right.left
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Contai... | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.left
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | . intro a
exists C.N i node a
simp only [toContainer] at a
exists (by
cases hix
have : nx = node := by
apply congrArg Sigma.fst hβ
cases this
have hβ := Sigma.snd_equals _ _ _ hβ
have wfx' := wfx' a
cases hβ
exact wfx'
)
exists (by
cases hiy
have... | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | cases hiy | case hβ.right.left
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Contai... | case hβ.right.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Co... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.left
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have hny: ny = node := by
apply congrArg Sigma.fst hβ | case hβ.right.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Co... | case hβ.right.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Co... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | cases hny | case hβ.right.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Co... | case hβ.right.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.left.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have hβ := Sigma.snd_equals _ _ _ hβ | case hβ.right.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ... | case hβ.right.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | rw [β hβ] | case hβ.right.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ... | case hβ.right.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | rfl | case hβ.right.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.left.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | apply congrArg Sigma.fst hβ | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toContainer C... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | intro a | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exists C.N i node a | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | simp only [toContainer] at a | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exists (by
cases hix
have : nx = node := by
apply congrArg Sigma.fst hβ
cases this
have hβ := Sigma.snd_equals _ _ _ hβ
have wfx' := wfx' a
cases hβ
exact wfx'
) | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exists (by
cases hiy
have : ny = node := by
apply congrArg Sigma.fst hβ
cases this
have hβ := Sigma.snd_equals _ _ _ hβ
have wfy' := wfy' a
cases hβ
exact wfy'
) | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exact hβ a | case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Conta... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.right.right
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | cases hix | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toContainer ... | case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toC... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have : nx = node := by
apply congrArg Sigma.fst hβ | case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toC... | case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toC... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | cases this | case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toC... | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have hβ := Sigma.snd_equals _ _ _ hβ | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have wfx' := wfx' a | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | cases hβ | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | case refl.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Contai... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exact wfx' | case refl.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Contai... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | apply congrArg Sigma.fst hβ | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toContainer C... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | cases hiy | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toContainer ... | case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toC... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have : ny = node := by
apply congrArg Sigma.fst hβ | case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toC... | case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toC... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | cases this | case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toC... | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have hβ := Sigma.snd_equals _ _ _ hβ | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | have wfy' := wfy' a | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | cases hβ | case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M... | case refl.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Contai... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | exact wfy' | case refl.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Contai... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.refl.refl
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.bisim | [85, 1] | [162, 13] | apply congrArg Sigma.fst hβ | I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C i node z) (kβ z) (kβ z)
i : I
xβ : Container.M (toContainer C... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C i node), R (N C ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.congr.coinduction | [55, 1] | [66, 13] | intro hβ i x y hβ | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
β’ (β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y) β β (i : I) (x y : M (C F) i), p i x y β congr F i x y | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
β’ congr F i x y | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
β’ (β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y) β β (i : I) (x y : M (C F) i), p i x y β congr F i x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.congr.coinduction | [55, 1] | [66, 13] | simp only [congr, pcongr] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
β’ congr F i x y | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
β’ β(pgfp (precongr F)) β₯ i x y | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
β’ congr F i x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.congr.coinduction | [55, 1] | [66, 13] | have := (pgfp.coinduction (precongr F) p).2 | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
β’ β(pgfp (precongr F)) β₯ i x y | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ β(pgfp (precongr F)) β₯ i x y | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
β’ β(pgfp (precongr F)) β₯ i x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.congr.coinduction | [55, 1] | [66, 13] | apply this | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ β(pgfp (precongr F)) β₯ i x y | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ p β€ β(precongr F) (p β β(p... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.congr.coinduction | [55, 1] | [66, 13] | have : p β€ p β pgfp (precongr F) p := by
simp | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ p β€ β(precongr F) (p β β(p... | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
thisβ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
this : p β€ p β β(pgfp (prec... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F))... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.congr.coinduction | [55, 1] | [66, 13] | have := (precongr F).2 this | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
thisβ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
this : p β€ p β β(pgfp (prec... | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
thisβ : p β€ p β β(pgfp (pr... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
thisβ : p β€ β(precongr F) (p β β(pgfp (precongr F)... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.congr.coinduction | [55, 1] | [66, 13] | apply le_trans _ this | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
thisβ : p β€ p β β(pgfp (pr... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
thisβ : p β€ p β β(pgfp (precongr ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.congr.coinduction | [55, 1] | [66, 13] | apply hβ | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
thisβ : p β€ p β β(pgfp (precongr ... | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ p i x y | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
thisβΒΉ : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.congr.coinduction | [55, 1] | [66, 13] | assumption | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ p i x y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F))... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.congr.coinduction | [55, 1] | [66, 13] | simp | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p β€ β(pgfp (precongr F)) β₯
β’ p β€ p β β(pgfp (precongr F)) p | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
p : (i : I) β M (C F) i β M (C F) i β Prop
hβ : β (i : I) (x y : M (C F) i), p i x y β β(precongr F) p i x y
i : I
x y : M (C F) i
hβ : p i x y
this : p β€ β(precongr F) (p β β(pgfp (precongr F)) p) β p... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.destruct_corec | [97, 1] | [103, 47] | simp only [IQPF.M.destruct, IQPF.M.corec, destruct.f, IContainer.M.destruct_corec, inst.abs_imap, inst.abs_repr] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
Ξ± : I β Type uβ
f : (i : I) β Ξ± i β F Ξ± i
i : I
xβ : Ξ± i
β’ destruct (corec f xβ) = IFunctor.imap (fun i x => corec f x) (f i xβ) | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
Ξ± : I β Type uβ
f : (i : I) β Ξ± i β F Ξ± i
i : I
xβ : Ξ± i
β’ IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1)
(IFunctor.imap (fun i => IContainer.M.corec fun i x => repr (f i x)) (f i xβ)) =
IFunctor.imap (fun i x => Quot.mk (congr F i) (IContainer.M... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
Ξ± : I β Type uβ
f : (i : I) β Ξ± i β F Ξ± i
i : I
xβ : Ξ± i
β’ destruct (corec f xβ) = IFunctor.imap (fun i x => corec f x) (f i xβ)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.destruct_corec | [97, 1] | [103, 47] | rw [βinst.abs_repr (f i xβ)] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
Ξ± : I β Type uβ
f : (i : I) β Ξ± i β F Ξ± i
i : I
xβ : Ξ± i
β’ IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1)
(IFunctor.imap (fun i => IContainer.M.corec fun i x => repr (f i x)) (f i xβ)) =
IFunctor.imap (fun i x => Quot.mk (congr F i) (IContainer.M... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
Ξ± : I β Type uβ
f : (i : I) β Ξ± i β F Ξ± i
i : I
xβ : Ξ± i
β’ IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1)
(IFunctor.imap (fun i => IContainer.M.corec fun i x => repr (f i x)) (abs (repr (f i xβ)))) =
IFunctor.imap (fun i x => Quot.mk (congr F i) ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
Ξ± : I β Type uβ
f : (i : I) β Ξ± i β F Ξ± i
i : I
xβ : Ξ± i
β’ IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1)
(IFunctor.imap (fun i => IContainer.M.corec fun i x => repr (f i x)) (f i xβ)) =
... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.destruct_corec | [97, 1] | [103, 47] | cases repr (f i xβ) with
| mk n k =>
simp only [βinst.abs_imap, IContainer.Map] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
Ξ± : I β Type uβ
f : (i : I) β Ξ± i β F Ξ± i
i : I
xβ : Ξ± i
β’ IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1)
(IFunctor.imap (fun i => IContainer.M.corec fun i x => repr (f i x)) (abs (repr (f i xβ)))) =
IFunctor.imap (fun i x => Quot.mk (congr F i) ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
Ξ± : I β Type uβ
f : (i : I) β Ξ± i β F Ξ± i
i : I
xβ : Ξ± i
β’ IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1)
(IFunctor.imap (fun i => IContainer.M.corec fun i x => repr (f i x)) (abs (repr (f ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.destruct_corec | [97, 1] | [103, 47] | simp only [βinst.abs_imap, IContainer.Map] | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
Ξ± : I β Type uβ
f : (i : I) β Ξ± i β F Ξ± i
i : I
xβ : Ξ± i
n : IContainer.A (C F) i
k : (y : IContainer.B (C F) i n) β Ξ± (IContainer.N (C F) i n y)
β’ IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1)
(IFunctor.imap (fun i => IContainer.M.corec fun... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
Ξ± : I β Type uβ
f : (i : I) β Ξ± i β F Ξ± i
i : I
xβ : Ξ± i
n : IContainer.A (C F) i
k : (y : IContainer.B (C F) i n) β Ξ± (IContainer.N (C F) i n y)
β’ IFunctor.imap (fun x x_1 => Quot.mk (congr F ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.imap_spec | [118, 1] | [124, 40] | conv =>
congr
<;> rw [βinst.abs_repr x] | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
x : F Ξ± i
β’ IFunctor.imap (fun i => f i β g i) x = IFunctor.imap f (IFunctor.imap g x) | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
x : F Ξ± i
β’ IFunctor.imap (fun i => f i β g i) (abs (repr x)) = IFunctor.imap f (IFunctor.imap g (abs (repr x))) | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
x : F Ξ± i
β’ IFunctor.imap (fun i => f i β g i) x = IFunctor.imap f (IFunctor.imap g x)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.imap_spec | [118, 1] | [124, 40] | cases repr x | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
x : F Ξ± i
β’ IFunctor.imap (fun i => f i β g i) (abs (repr x)) = IFunctor.imap f (IFunctor.imap g (abs (repr x))) | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
x : F Ξ± i
fstβ : IContainer.A (C F) i
sndβ : (y : IContainer.B (C F) i fstβ) β Ξ± (IContainer.N (C F) i fstβ y)
β’ IFunctor.imap (fun i => f i β g i) (abs { fst := fstβ, snd := sndβ ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
x : F Ξ± i
β’ IFunctor.imap (fun i => f i β g i) (abs (repr x)) = IFunctor.imap f (IFunctor.imap g (abs (repr x)))
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.imap_spec | [118, 1] | [124, 40] | simp [βinst.abs_imap, IContainer.Map] | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
x : F Ξ± i
fstβ : IContainer.A (C F) i
sndβ : (y : IContainer.B (C F) i fstβ) β Ξ± (IContainer.N (C F) i fstβ y)
β’ IFunctor.imap (fun i => f i β g i) (abs { fst := fstβ, snd := sndβ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
x : F Ξ± i
fstβ : IContainer.A (C F) i
sndβ : (y : IContainer.B (C F) i fstβ) β Ξ± (IContainer.N (C F) i fstβ y)
β’ IFunct... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IContainer.Map_spec | [126, 1] | [129, 24] | cases x | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
x : Obj (IQPF.C F) Ξ± i
β’ Map (fun i => f i β g i) x = Map f (Map g x) | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
fstβ : A (IQPF.C F) i
sndβ : (y : B (IQPF.C F) i fstβ) β Ξ± (N (IQPF.C F) i fstβ y)
β’ Map (fun i => f i β g i) { fst := fstβ, snd := sndβ } = Map f (Map g { fst := fstβ, snd := sndβ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
x : Obj (IQPF.C F) Ξ± i
β’ Map (fun i => f i β g i) x = Map f (Map g x)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IContainer.Map_spec | [126, 1] | [129, 24] | simp [IContainer.Map] | case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
fstβ : A (IQPF.C F) i
sndβ : (y : B (IQPF.C F) i fstβ) β Ξ± (N (IQPF.C F) i fstβ y)
β’ Map (fun i => f i β g i) { fst := fstβ, snd := sndβ } = Map f (Map g { fst := fstβ, snd := sndβ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
i : I
Ξ± Ξ² Ξ³ : I β Type uβ
f : (i : I) β Ξ² i β Ξ³ i
g : (i : I) β Ξ± i β Ξ² i
fstβ : A (IQPF.C F) i
sndβ : (y : B (IQPF.C F) i fstβ) β Ξ± (N (IQPF.C F) i fstβ y)
β’ Map (fun i => f i β g i) { fst := ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | intro i x | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
β’ β (i : I) (x y : M F i), r i x y β x ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x : M F i
β’ β (y : M F i), r i x ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply Quot.inductionOn (motive := _) x | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x : M F i
β’ β (y : M F i), r i x ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x : M F i
β’ β (a : IContainer.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | clear x | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x : M F i
β’ β (a : IContainer.M (... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
β’ β (a : IContainer.M (C F) i) (y... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | intro x y | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
β’ β (a : IContainer.M (C F) i) (y... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x : IContainer.M (C F) i
y : M F ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply Quot.inductionOn (motive := _) y | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x : IContainer.M (C F) i
y : M F ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x : IContainer.M (C F) i
y : M F ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | clear y | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x : IContainer.M (C F) i
y : M F ... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x : IContainer.M (C F) i
β’ β (a :... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | intro y hβ | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x : IContainer.M (C F) i
β’ β (a :... | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F) i
hβ : r... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | apply Quot.sound | I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F) i
hβ : r... | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F) i... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.m... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/MIdx.lean | IQPF.M.bisim_lemma | [131, 1] | [183, 13] | let r' i x y := r i (Quot.mk _ x) (Quot.mk _ y) | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F) i... | case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i : I
x y : IContainer.M (C F) i... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
F : (I β Type uβ) β I β Type uβ
inst : IQPF F
r : (i : I) β M F i β M F i β Prop
hβ : β (i : I) (x : M F i), r i x x
hβ :
β (i : I) (x y : M F i),
r i x y β IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i =>... |
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