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/M.lean | Container.M.bisim.lemma0 | [121, 1] | [131, 52] | apply HEq.symm | case h
C : Container
x : M C
n : Nat
i : B C (Approx.node (approx x (Nat.succ n)))
j : B C (destruct x).fst
heq : HEq i j
this : B C (destruct x).fst = B C (Approx.node (approx x (Nat.succ n)))
β’ HEq j i | case h.h
C : Container
x : M C
n : Nat
i : B C (Approx.node (approx x (Nat.succ n)))
j : B C (destruct x).fst
heq : HEq i j
this : B C (destruct x).fst = B C (Approx.node (approx x (Nat.succ n)))
β’ HEq i j | Please generate a tactic in lean4 to solve the state.
STATE:
case h
C : Container
x : M C
n : Nat
i : B C (Approx.node (approx x (Nat.succ n)))
j : B C (destruct x).fst
heq : HEq i j
this : B C (destruct x).fst = B C (Approx.node (approx x (Nat.succ n)))
β’ HEq j i
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma0 | [121, 1] | [131, 52] | assumption | case h.h
C : Container
x : M C
n : Nat
i : B C (Approx.node (approx x (Nat.succ n)))
j : B C (destruct x).fst
heq : HEq i j
this : B C (destruct x).fst = B C (Approx.node (approx x (Nat.succ n)))
β’ HEq i j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
C : Container
x : M C
n : Nat
i : B C (Approx.node (approx x (Nat.succ n)))
j : B C (destruct x).fst
heq : HEq i j
this : B C (destruct x).fst = B C (Approx.node (approx x (Nat.succ n)))
β’ HEq i j
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | intro x y n hβ | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
β’ β (x y : M C) (n : Nat), R x y β approx x n = approx y n | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
n : Nat
hβ : R x y
β’ approx x n = approx y n | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
β’ β (x y : M C) (n : Nat), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | induction n generalizing x y | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
n : Nat
hβ : R x y
β’ approx x n = approx y n | case zero
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ approx x Nat.zero = approx y Nat.zero
case succ
C : Container... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
n : Nat
hβ : R x y
β’ app... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | case zero =>
cases x.approx 0
cases y.approx 0
rfl | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ approx x Nat.zero = approx y Nat.zero | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ approx x Na... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | case succ n h =>
have hβ := x.node_thm n
have hβ := y.node_thm n
cases hβ: x.approx (.succ n) with
| MStep nodex cx =>
cases hβ
: y.approx (.succ n) with
| MStep nodey cy =>
have β¨node, kβ, kβ, eqβ, eqβ, kRβ© := hβ _ _ hβ
have hβ : (Approx.MStep nodex cx).node = node := by
have := cong... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
β’ approx x (Nat... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | cases x.approx 0 | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ approx x Nat.zero = approx y Nat.zero | case MStop
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ Approx.MStop = approx y Nat.zero | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ approx x Na... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | cases y.approx 0 | case MStop
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ Approx.MStop = approx y Nat.zero | case MStop.MStop
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ Approx.MStop = Approx.MStop | Please generate a tactic in lean4 to solve the state.
STATE:
case MStop
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rfl | case MStop.MStop
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ Approx.MStop = Approx.MStop | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case MStop.MStop
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have hβ := x.node_thm n | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
β’ approx x (Nat... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have hβ := y.node_thm n | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | cases hβ: x.approx (.succ n) with
| MStep nodex cx =>
cases hβ
: y.approx (.succ n) with
| MStep nodey cy =>
have β¨node, kβ, kβ, eqβ, eqβ, kRβ© := hβ _ _ hβ
have hβ : (Approx.MStep nodex cx).node = node := by
have := congrArg (Ξ» x => x.1) eqβ
simp only [destruct] at this
rw [hβ] at hβ
... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | cases hβ
: y.approx (.succ n) with
| MStep nodey cy =>
have β¨node, kβ, kβ, eqβ, eqβ, kRβ© := hβ _ _ hβ
have hβ : (Approx.MStep nodex cx).node = node := by
have := congrArg (Ξ» x => x.1) eqβ
simp only [destruct] at this
rw [hβ] at hβ
rw [βthis]
exact hβ
have hβ : (Approx.MStep nodey cy).node = nod... | case MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have β¨node, kβ, kβ, eqβ, eqβ, kRβ© := hβ _ _ hβ | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have hβ : (Approx.MStep nodex cx).node = node := by
have := congrArg (Ξ» x => x.1) eqβ
simp only [destruct] at this
rw [hβ] at hβ
rw [βthis]
exact hβ | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have hβ : (Approx.MStep nodey cy).node = node := by
have := congrArg (Ξ» x => x.1) eqβ
simp only [destruct] at this
rw [hβ
] at hβ
rw [βthis]
exact hβ | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | simp [Approx.node] at hβ hβ | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have hβ := Eq.symm hβ | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have hβ := Eq.symm hβ | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have hβ := bisim.lemma0 x n | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have hβ := bisim.lemma0 y n | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [hβ] at hβ | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [hβ
] at hβ | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | simp only [Approx.children] at hβ hβ | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | induction hβ | case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x ... | case MStep.MStep.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ :... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | induction hβ | case MStep.MStep.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ :... | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | suffices hβ : β i: C.B node, cx i = cy i by
have : cx = cy := by
funext i
apply hβ
rw [this] | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | intro i | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have hβ : β i, cx i = (kβ i).approx n := by
have h : β i j, HEq i j β (x.destruct.snd i) = kβ j := by
rw [eqβ]
intro i j heq
cases heq
rfl
intro i
rw [hβ i (cast (by simp [congrArg (Ξ» x => x.1) eqβ]) i)]
. rw [h]
apply cast_heq
. apply HEq.symm
apply cast_heq | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have hβ : β i, cy i = (kβ i).approx n := by
have h : β i j, HEq i j β (y.destruct.snd i) = kβ j := by
rw [eqβ]
intro i j heq
cases heq
rfl
intro i
rw [hβ i (cast (by simp [congrArg (Ξ» x => x.1) eqβ]) i)]
. rw [h]
apply cast_heq
. apply HEq.symm
apply cast_heq | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [hβ, hβ] | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | apply h | case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C... | case MStep.MStep.refl.refl.hβ
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep.refl.refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | apply kR | case MStep.MStep.refl.refl.hβ
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case MStep.MStep.refl.refl.hβ
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have := congrArg (Ξ» x => x.1) eqβ | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | simp only [destruct] at this | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [hβ] at hβ | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [βthis] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | exact hβ | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hβ : Approx.nod... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have := congrArg (Ξ» x => x.1) eqβ | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | simp only [destruct] at this | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [hβ
] at hβ | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [βthis] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | exact hβ | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have : cx = cy := by
funext i
apply hβ | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [this] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | funext i | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Ap... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | apply hβ | case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Ap... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have h : β i j, HEq i j β (x.destruct.snd i) = kβ j := by
rw [eqβ]
intro i j heq
cases heq
rfl | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | intro i | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [hβ i (cast (by simp [congrArg (Ξ» x => x.1) eqβ]) i)] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | . rw [h]
apply cast_heq | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | . apply HEq.symm
apply cast_heq | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [eqβ] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | intro i j heq | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | cases heq | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | case refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ :... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rfl | case refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | simp [congrArg (Ξ» x => x.1) eqβ] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [h] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | case a
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : A... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | apply cast_heq | case a
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : A... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | apply HEq.symm | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : A... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | apply cast_heq | case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : A... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | have h : β i j, HEq i j β (y.destruct.snd i) = kβ j := by
rw [eqβ]
intro i j heq
cases heq
rfl | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | intro i | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [hβ i (cast (by simp [congrArg (Ξ» x => x.1) eqβ]) i)] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | . rw [h]
apply cast_heq | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | . apply HEq.symm
apply cast_heq | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [eqβ] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | intro i j heq | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | cases heq | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.no... | case refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ :... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rfl | case refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
h : β (x y : M C... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | simp [congrArg (Ξ» x => x.1) eqβ] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | rw [h] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | case a
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : A... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | apply cast_heq | case a
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : A... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | apply HEq.symm | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : Approx.n... | case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : A... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim.lemma1 | [136, 1] | [219, 17] | apply cast_heq | case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C), R x y β approx x n = approx y n
x y : M C
hβ : R x y
hββ : A... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
n : Nat
hβ : β (x y : M C),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim | [221, 1] | [232, 35] | intro x y hβ | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
β’ β (x y : M C), R x y β x = y | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ x = y | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
β’ β (x y : M C), R x y β x = y
TAC... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim | [221, 1] | [232, 35] | suffices hβ: x.approx = y.approx by
cases x
cases y
simp only at hβ
simp [hβ] | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ x = y | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ x.approx = y.approx | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ x = y
TACTI... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim | [221, 1] | [232, 35] | funext n | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ x.approx = y.approx | case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
n : Nat
β’ approx x n = approx y n | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
β’ x.approx = ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim | [221, 1] | [232, 35] | apply bisim.lemma1 R hβ x y n hβ | case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
n : Nat
β’ approx x n = approx y n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
n : Na... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim | [221, 1] | [232, 35] | cases x | C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
hβ : x.approx = y.approx
β’ x = y | case mk
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
y : M C
approxβ : (n : Nat) β Approx C n
agreesβ : β (n : Nat), Agree (approxβ n) (appr... | Please generate a tactic in lean4 to solve the state.
STATE:
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
x y : M C
hβ : R x y
hβ : x.approx... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim | [221, 1] | [232, 35] | cases y | case mk
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
y : M C
approxβ : (n : Nat) β Approx C n
agreesβ : β (n : Nat), Agree (approxβ n) (appr... | case mk.mk
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
approxβΒΉ : (n : Nat) β Approx C n
agreesβΒΉ : β (n : Nat), Agree (approxβΒΉ n) (approx... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
y : M C
approxβ : (n : Nat... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim | [221, 1] | [232, 35] | simp only at hβ | case mk.mk
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
approxβΒΉ : (n : Nat) β Approx C n
agreesβΒΉ : β (n : Nat), Agree (approxβΒΉ n) (approx... | case mk.mk
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
approxβΒΉ : (n : Nat) β Approx C n
agreesβΒΉ : β (n : Nat), Agree (approxβΒΉ n) (approx... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
approxβΒΉ : (n : Nat) β ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/M.lean | Container.M.bisim | [221, 1] | [232, 35] | simp [hβ] | case mk.mk
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
approxβΒΉ : (n : Nat) β Approx C n
agreesβΒΉ : β (n : Nat), Agree (approxβΒΉ n) (approx... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk
C : Container
R : M C β M C β Prop
hβ :
β (x y : M C),
R x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (i : B C node), R (kβ i) (kβ i)
approxβΒΉ : (n : Nat) β ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.by_cases | [106, 15] | [113, 17] | intro x | F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
β’ (x : Free F R) β motive x | F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
x : Free F R
β’ motive x | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
β’ (x : Free F R) β motive x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.by_cases | [106, 15] | [113, 17] | rw [βconstruct_destruct x] | F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
x : Free F R
β’ motive x | F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
x : Free F R
β’ motive (construct (destruct x)) | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
x : Free F R
β’ motive x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.by_cases | [106, 15] | [113, 17] | cases destruct x with
| Pure r =>
exact pure r
| Free f =>
exact free f | F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
x : Free F R
β’ motive (construct (destruct x)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
x : Free F R
β’ motive (construct (destruct x))
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.by_cases | [106, 15] | [113, 17] | exact pure r | case Pure
F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
x : Free F R
r : R
β’ motive (construct (FreeF.Pure r)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Pure
F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
x : Free F R
r : R
β’ motive (construct (FreeF.Pure r))
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.by_cases | [106, 15] | [113, 17] | exact free f | case Free
F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
x : Free F R
f : F (Free F R)
β’ motive (construct (FreeF.Free f)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Free
F : Type u β Type u
inst : QPF F
R : Type u
motive : Free F R β Sort u_1
pure : (r : R) β motive (Pure.pure r)
free : (f : F (Free F R)) β motive (Free.free f)
x : Free F R
f : F (Free F R)
β’ motive (construct (FreeF.Free f))
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.destruct_pure | [115, 9] | [116, 34] | simp [pure, destruct_construct] | F : Type u β Type u
inst : QPF F
R : Type u
r : R
β’ destruct (pure r) = FreeF.Pure r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type u β Type u
inst : QPF F
R : Type u
r : R
β’ destruct (pure r) = FreeF.Pure r
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.destruct_free | [118, 9] | [119, 34] | simp [free, destruct_construct] | F : Type u β Type u
inst : QPF F
R : Type u
f : F (Free F R)
β’ destruct (free f) = FreeF.Free f | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type u β Type u
inst : QPF F
R : Type u
f : F (Free F R)
β’ destruct (free f) = FreeF.Free f
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.bind_inr.internal | [186, 1] | [205, 10] | apply QPF.M.bisim (Ξ» x y => corec (bind.automaton k) (.inr x) = y) | F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
β’ β (x y : Free F S), corec (bind.automaton k) (Sum.inr x) = y β x = y | F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
β’ β (x y : QPF.M (FreeF F S)),
corec (bind.automaton k) (Sum.inr x) = y β
QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
(QPF.M.destruct y) | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
β’ β (x y : Free F S), corec (bind.automaton k) (Sum.inr x) = y β x = y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.bind_inr.internal | [186, 1] | [205, 10] | . intro x y hβ
induction hβ
rw [corec, QPF.M.destruct_corec]
conv =>
congr
. skip
. skip
. rhs
simp only [bind.automaton]
exists (Ξ» x => β¨β¨x, corec (bind.automaton k) (.inr x)β©, by rflβ©) <$> destruct x
rw [destruct]
constructor
. simp only [βQPF.map_comp, Function.comp]
apply Eq.... | F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
β’ β (x y : QPF.M (FreeF F S)),
corec (bind.automaton k) (Sum.inr x) = y β
QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
(QPF.M.destruct y) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
β’ β (x y : QPF.M (FreeF F S)),
corec (bind.automaton k) (Sum.inr x) = y β
QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
(QPF.M.... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.bind_inr.internal | [186, 1] | [205, 10] | intro x y hβ | F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
β’ β (x y : QPF.M (FreeF F S)),
corec (bind.automaton k) (Sum.inr x) = y β
QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
(QPF.M.destruct y) | F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
hβ : corec (bind.automaton k) (Sum.inr x) = y
β’ QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x) (QPF.M.destruct y) | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
β’ β (x y : QPF.M (FreeF F S)),
corec (bind.automaton k) (Sum.inr x) = y β
QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
(QPF.M.... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.bind_inr.internal | [186, 1] | [205, 10] | induction hβ | F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
hβ : corec (bind.automaton k) (Sum.inr x) = y
β’ QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x) (QPF.M.destruct y) | case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
(QPF.M.destruct (corec (bind.automaton k) (Sum.inr x))) | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
hβ : corec (bind.automaton k) (Sum.inr x) = y
β’ QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x) (QPF.M.destruct y)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.bind_inr.internal | [186, 1] | [205, 10] | rw [corec, QPF.M.destruct_corec] | case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
(QPF.M.destruct (corec (bind.automaton k) (Sum.inr x))) | case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ QPF.M.liftr (FreeF F S) (fun x y => QPF.M.corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
((fun x => QPF.M.corec (bind.automaton k) x) <$> bind.automaton k (Sum.inr x)) | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ QPF.M.liftr (FreeF F S) (fun x y => corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
(QPF.M.destruct (corec (bind.automaton k) (Sum.inr x)))
TAC... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.bind_inr.internal | [186, 1] | [205, 10] | conv =>
congr
. skip
. skip
. rhs
simp only [bind.automaton] | case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ QPF.M.liftr (FreeF F S) (fun x y => QPF.M.corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
((fun x => QPF.M.corec (bind.automaton k) x) <$> bind.automaton k (Sum.inr x)) | case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ QPF.M.liftr (FreeF F S) (fun x y => QPF.M.corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
((fun x => QPF.M.corec (bind.automaton k) x) <$> Sum.inr <$> destruct x) | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ QPF.M.liftr (FreeF F S) (fun x y => QPF.M.corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
((fun x => QPF.M.corec (bind.automaton k) x) <$> bind... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.bind_inr.internal | [186, 1] | [205, 10] | exists (Ξ» x => β¨β¨x, corec (bind.automaton k) (.inr x)β©, by rflβ©) <$> destruct x | case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ QPF.M.liftr (FreeF F S) (fun x y => QPF.M.corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
((fun x => QPF.M.corec (bind.automaton k) x) <$> Sum.inr <$> destruct x) | case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ (fun x => (βx).fst) <$>
(fun x =>
{ val := (x, corec (bind.automaton k) (Sum.inr x)),
property :=
(_ :
QPF.M.corec (bind.automaton k) (Sum.inr (x, corec ... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ QPF.M.liftr (FreeF F S) (fun x y => QPF.M.corec (bind.automaton k) (Sum.inr x) = y) (QPF.M.destruct x)
((fun x => QPF.M.corec (bind.automaton k) x) <$> Sum.... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.bind_inr.internal | [186, 1] | [205, 10] | rw [destruct] | case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ (fun x => (βx).fst) <$>
(fun x =>
{ val := (x, corec (bind.automaton k) (Sum.inr x)),
property :=
(_ :
QPF.M.corec (bind.automaton k) (Sum.inr (x, corec ... | case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ (fun x => (βx).fst) <$>
(fun x =>
{ val := (x, corec (bind.automaton k) (Sum.inr x)),
property :=
(_ :
QPF.M.corec (bind.automaton k) (Sum.inr (x, corec ... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ (fun x => (βx).fst) <$>
(fun x =>
{ val := (x, corec (bind.automaton k) (Sum.inr x)),
property :=
(_ :
... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.bind_inr.internal | [186, 1] | [205, 10] | constructor | case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ (fun x => (βx).fst) <$>
(fun x =>
{ val := (x, corec (bind.automaton k) (Sum.inr x)),
property :=
(_ :
QPF.M.corec (bind.automaton k) (Sum.inr (x, corec ... | case refl.left
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ (fun x => (βx).fst) <$>
(fun x =>
{ val := (x, corec (bind.automaton k) (Sum.inr x)),
property :=
(_ :
QPF.M.corec (bind.automaton k) (Sum.inr (x, corec (bind... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ (fun x => (βx).fst) <$>
(fun x =>
{ val := (x, corec (bind.automaton k) (Sum.inr x)),
property :=
(_ :
... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/QPF/FreeMonads.lean | Free.bind_inr.internal | [186, 1] | [205, 10] | . simp only [βQPF.map_comp, Function.comp]
apply Eq.trans _ (QPF.map_id _)
rfl | case refl.left
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ (fun x => (βx).fst) <$>
(fun x =>
{ val := (x, corec (bind.automaton k) (Sum.inr x)),
property :=
(_ :
QPF.M.corec (bind.automaton k) (Sum.inr (x, corec (bind... | case refl.right
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ (fun x => (βx).snd) <$>
(fun x =>
{ val := (x, corec (bind.automaton k) (Sum.inr x)),
property :=
(_ :
QPF.M.corec (bind.automaton k) (Sum.inr (x, corec (bin... | Please generate a tactic in lean4 to solve the state.
STATE:
case refl.left
F : Type u β Type u
inst : QPF F
R S : Type u
k : R β Free F S
x y : QPF.M (FreeF F S)
β’ (fun x => (βx).fst) <$>
(fun x =>
{ val := (x, corec (bind.automaton k) (Sum.inr x)),
property :=
(_ :
... |
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