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/FreeMonads.lean | Free.eq.bisim | [136, 1] | [158, 12] | intro x | case hβ.Pure.refl
C : _root_.Container
R : Type uβ
x y : R
β’ β (i : Container.B (Container C R) (A.Pure x)),
eq (PEmpty.rec (fun x => M (Container C R)) i) (PEmpty.rec (fun x => M (Container C R)) i) | case hβ.Pure.refl
C : _root_.Container
R : Type uβ
xβ y : R
x : Container.B (Container C R) (A.Pure xβ)
β’ eq (PEmpty.rec (fun x => M (Container C R)) x) (PEmpty.rec (fun x => M (Container C R)) x) | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.Pure.refl
C : _root_.Container
R : Type uβ
x y : R
β’ β (i : Container.B (Container C R) (A.Pure x)),
eq (PEmpty.rec (fun x => M (Container C R)) i) (PEmpty.rec (fun x => M (Container C R)) i)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.bisim | [136, 1] | [158, 12] | apply x.elim | case hβ.Pure.refl
C : _root_.Container
R : Type uβ
xβ y : R
x : Container.B (Container C R) (A.Pure xβ)
β’ eq (PEmpty.rec (fun x => M (Container C R)) x) (PEmpty.rec (fun x => M (Container C R)) x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.Pure.refl
C : _root_.Container
R : Type uβ
xβ y : R
x : Container.B (Container C R) (A.Pure xβ)
β’ eq (PEmpty.rec (fun x => M (Container C R)) x) (PEmpty.rec (fun x => M (Container C R)) x)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.bisim | [136, 1] | [158, 12] | exists (A.Free node) | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β node_1 kβ_1 kβ_1,
M.destruct (construct (Functor.Free node kβ)) = { fst := node_1, snd := kβ_1 } β§
M.destruct (construct (Functor.Free n... | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β kβ_1 kβ_1,
M.destruct (construct (Functor.Free node kβ)) = { fst := A.Free node, snd := kβ_1 } β§
M.destruct (construct (Functor.Free nod... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β node_1 kβ_1 kβ_1,
M.destruct (construct (Functor.Free node kβ)) = { fst := node_1... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.bisim | [136, 1] | [158, 12] | exists kβ | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β kβ_1 kβ_1,
M.destruct (construct (Functor.Free node kβ)) = { fst := A.Free node, snd := kβ_1 } β§
M.destruct (construct (Functor.Free nod... | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β kβ_1,
M.destruct (construct (Functor.Free node kβ)) = { fst := A.Free node, snd := kβ } β§
M.destruct (construct (Functor.Free node kβ)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β kβ_1 kβ_1,
M.destruct (construct (Functor.Free node kβ)) = { fst := A.Free node, ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.bisim | [136, 1] | [158, 12] | exists kβ | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β kβ_1,
M.destruct (construct (Functor.Free node kβ)) = { fst := A.Free node, snd := kβ } β§
M.destruct (construct (Functor.Free node kβ)) ... | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ M.destruct (construct (Functor.Free node kβ)) = { fst := A.Free node, snd := kβ } β§
M.destruct (construct (Functor.Free node kβ)) = { fst := A.F... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β kβ_1,
M.destruct (construct (Functor.Free node kβ)) = { fst := A.Free node, snd :... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.bisim | [136, 1] | [158, 12] | simp only [construct, M.destruct_construct, inv, true_and] | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ M.destruct (construct (Functor.Free node kβ)) = { fst := A.Free node, snd := kβ } β§
M.destruct (construct (Functor.Free node kβ)) = { fst := A.F... | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β (i : Container.B (Container C R) (A.Free node)), eq (kβ i) (kβ i) | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ M.destruct (construct (Functor.Free node kβ)) = { fst := A.Free node, snd := kβ } β§
... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.bisim | [136, 1] | [158, 12] | intro x | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β (i : Container.B (Container C R) (A.Free node)), eq (kβ i) (kβ i) | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
x : Container.B (Container C R) (A.Free node)
β’ eq (kβ x) (kβ x) | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
β’ β (i : Container.B (Container C R) (A.Free node)), eq (kβ i) (kβ i)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.bisim | [136, 1] | [158, 12] | rw [CompleteLattice.bot_sup] at h | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
x : Container.B (Container C R) (A.Free node)
β’ eq (kβ x) (kβ x) | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), β(pgfp (equivF' Eq)) β₯ (kβ x) (kβ x)
x : Container.B (Container C R) (A.Free node)
β’ eq (kβ x) (kβ x) | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), (β₯ β β(pgfp (equivF' Eq)) β₯) (kβ x) (kβ x)
x : Container.B (Container C R) (A.Free node)
β’ eq (kβ x) (kβ x)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.bisim | [136, 1] | [158, 12] | apply h | case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), β(pgfp (equivF' Eq)) β₯ (kβ x) (kβ x)
x : Container.B (Container C R) (A.Free node)
β’ eq (kβ x) (kβ x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ.Free
C : _root_.Container
R : Type uβ
node : C.A
kβ kβ : Container.B C node β Free C R
h : β (x : Container.B C node), β(pgfp (equivF' Eq)) β₯ (kβ x) (kβ x)
x : Container.B (Container C R) (A.Free node)
β’ eq (kβ x) (kβ x)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | have : β (x y:Free C R), x = y β Free.eq x y := by
apply Free.equiv.coinduction
intro x y h
cases h
conv =>
congr
. rfl
. rfl
. rw [βconstruct_destruct x]
. rw [βconstruct_destruct x]
cases destruct x with
| Pure r =>
apply equivF.Pure
rfl
| Free node k =>
apply equivF.Free... | C : _root_.Container
R : Type uβ
β’ β (x : Free C R), eq x x | C : _root_.Container
R : Type uβ
this : β (x y : Free C R), x = y β eq x y
β’ β (x : Free C R), eq x x | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R : Type uβ
β’ β (x : Free C R), eq x x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | intro x | C : _root_.Container
R : Type uβ
this : β (x y : Free C R), x = y β eq x y
β’ β (x : Free C R), eq x x | C : _root_.Container
R : Type uβ
this : β (x y : Free C R), x = y β eq x y
x : Free C R
β’ eq x x | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R : Type uβ
this : β (x y : Free C R), x = y β eq x y
β’ β (x : Free C R), eq x x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | apply this | C : _root_.Container
R : Type uβ
this : β (x y : Free C R), x = y β eq x y
x : Free C R
β’ eq x x | case a
C : _root_.Container
R : Type uβ
this : β (x y : Free C R), x = y β eq x y
x : Free C R
β’ x = x | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R : Type uβ
this : β (x y : Free C R), x = y β eq x y
x : Free C R
β’ eq x x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | rfl | case a
C : _root_.Container
R : Type uβ
this : β (x y : Free C R), x = y β eq x y
x : Free C R
β’ x = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R : Type uβ
this : β (x y : Free C R), x = y β eq x y
x : Free C R
β’ x = x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | apply Free.equiv.coinduction | C : _root_.Container
R : Type uβ
β’ β (x y : Free C R), x = y β eq x y | case a
C : _root_.Container
R : Type uβ
β’ β (x y : Free C R), x = y β equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) x y | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R : Type uβ
β’ β (x y : Free C R), x = y β eq x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | intro x y h | case a
C : _root_.Container
R : Type uβ
β’ β (x y : Free C R), x = y β equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) x y | case a
C : _root_.Container
R : Type uβ
x y : Free C R
h : x = y
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) x y | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R : Type uβ
β’ β (x y : Free C R), x = y β equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | cases h | case a
C : _root_.Container
R : Type uβ
x y : Free C R
h : x = y
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) x y | case a.refl
C : _root_.Container
R : Type uβ
x : Free C R
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) x x | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R : Type uβ
x y : Free C R
h : x = y
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | conv =>
congr
. rfl
. rfl
. rw [βconstruct_destruct x]
. rw [βconstruct_destruct x] | case a.refl
C : _root_.Container
R : Type uβ
x : Free C R
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) x x | case a.refl
C : _root_.Container
R : Type uβ
x : Free C R
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) (construct (destruct x)) (construct (destruct x)) | Please generate a tactic in lean4 to solve the state.
STATE:
case a.refl
C : _root_.Container
R : Type uβ
x : Free C R
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) x x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | cases destruct x with
| Pure r =>
apply equivF.Pure
rfl
| Free node k =>
apply equivF.Free
intro y
left
rfl | case a.refl
C : _root_.Container
R : Type uβ
x : Free C R
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) (construct (destruct x)) (construct (destruct x)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.refl
C : _root_.Container
R : Type uβ
x : Free C R
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) (construct (destruct x)) (construct (destruct x))
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | apply equivF.Pure | case a.refl.Pure
C : _root_.Container
R : Type uβ
x : Free C R
r : R
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) (construct (Functor.Pure r)) (construct (Functor.Pure r)) | case a.refl.Pure.a
C : _root_.Container
R : Type uβ
x : Free C R
r : R
β’ r = r | Please generate a tactic in lean4 to solve the state.
STATE:
case a.refl.Pure
C : _root_.Container
R : Type uβ
x : Free C R
r : R
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) (construct (Functor.Pure r)) (construct (Functor.Pure r))
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | rfl | case a.refl.Pure.a
C : _root_.Container
R : Type uβ
x : Free C R
r : R
β’ r = r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.refl.Pure.a
C : _root_.Container
R : Type uβ
x : Free C R
r : R
β’ r = r
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | apply equivF.Free | case a.refl.Free
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) (construct (Functor.Free node k))
(construct (Functor.Free node k)) | case a.refl.Free.a
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
β’ β (x : Container.B C node), ((fun x y => x = y) β pequiv Eq fun x y => x = y) (k x) (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case a.refl.Free
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
β’ equivF Eq ((fun x y => x = y) β pequiv Eq fun x y => x = y) (construct (Functor.Free node k))
(construct (Functor.Free node k))
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | intro y | case a.refl.Free.a
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
β’ β (x : Container.B C node), ((fun x y => x = y) β pequiv Eq fun x y => x = y) (k x) (k x) | case a.refl.Free.a
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
y : Container.B C node
β’ ((fun x y => x = y) β pequiv Eq fun x y => x = y) (k y) (k y) | Please generate a tactic in lean4 to solve the state.
STATE:
case a.refl.Free.a
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
β’ β (x : Container.B C node), ((fun x y => x = y) β pequiv Eq fun x y => x = y) (k x) (k x)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | left | case a.refl.Free.a
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
y : Container.B C node
β’ ((fun x y => x = y) β pequiv Eq fun x y => x = y) (k y) (k y) | case a.refl.Free.a.h
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
y : Container.B C node
β’ (fun x y => x = y) (k y) (k y) | Please generate a tactic in lean4 to solve the state.
STATE:
case a.refl.Free.a
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
y : Container.B C node
β’ ((fun x y => x = y) β pequiv Eq fun x y => x = y) (k y) (k y)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.eq.rfl | [161, 1] | [183, 6] | rfl | case a.refl.Free.a.h
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
y : Container.B C node
β’ (fun x y => x = y) (k y) (k y) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.refl.Free.a.h
C : _root_.Container
R : Type uβ
x : Free C R
node : C.A
k : Container.B C node β Free C R
y : Container.B C node
β’ (fun x y => x = y) (k y) (k y)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | apply Free.eq.bisim | C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
β’ corec (bind.automaton f) (Sum.inr x) = x | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
β’ eq (corec (bind.automaton f) (Sum.inr x)) x | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
β’ corec (bind.automaton f) (Sum.inr x) = x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | have : β x y, x = corec (bind.automaton f) (.inr y) β eq x y := by
apply Free.equiv.coinduction
intro x y hβ
conv =>
congr
. rfl
. rfl
. rw [βconstruct_destruct x]
. rw [βconstruct_destruct y]
have hβ := congrArg destruct hβ
clear hβ
rw [destruct_corec] at hβ
cases hy: destruct y with
... | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
β’ eq (corec (bind.automaton f) (Sum.inr x)) x | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
this : β (x y : Free C S), x = corec (bind.automaton f) (Sum.inr y) β eq x y
β’ eq (corec (bind.automaton f) (Sum.inr x)) x | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
β’ eq (corec (bind.automaton f) (Sum.inr x)) x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | apply this | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
this : β (x y : Free C S), x = corec (bind.automaton f) (Sum.inr y) β eq x y
β’ eq (corec (bind.automaton f) (Sum.inr x)) x | case a.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
this : β (x y : Free C S), x = corec (bind.automaton f) (Sum.inr y) β eq x y
β’ corec (bind.automaton f) (Sum.inr x) = corec (bind.automaton f) (Sum.inr x) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
this : β (x y : Free C S), x = corec (bind.automaton f) (Sum.inr y) β eq x y
β’ eq (corec (bind.automaton f) (Sum.inr x)) x
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | rfl | case a.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
this : β (x y : Free C S), x = corec (bind.automaton f) (Sum.inr y) β eq x y
β’ corec (bind.automaton f) (Sum.inr x) = corec (bind.automaton f) (Sum.inr x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
this : β (x y : Free C S), x = corec (bind.automaton f) (Sum.inr y) β eq x y
β’ corec (bind.automaton f) (Sum.inr x) = corec (bind.automaton f) (Sum.inr x)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | apply Free.equiv.coinduction | C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
β’ β (x y : Free C S), x = corec (bind.automaton f) (Sum.inr y) β eq x y | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
β’ β (x y : Free C S),
x = corec (bind.automaton f) (Sum.inr y) β
equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
x y | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
β’ β (x y : Free C S), x = corec (bind.automaton f) (Sum.inr y) β eq x y
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | intro x y hβ | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
β’ β (x y : Free C S),
x = corec (bind.automaton f) (Sum.inr y) β
equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
x y | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : x = corec (bind.automaton f) (Sum.inr y)
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
x y | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
x : Free C S
β’ β (x y : Free C S),
x = corec (bind.automaton f) (Sum.inr y) β
equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = co... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | conv =>
congr
. rfl
. rfl
. rw [βconstruct_destruct x]
. rw [βconstruct_destruct y] | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : x = corec (bind.automaton f) (Sum.inr y)
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
x y | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : x = corec (bind.automaton f) (Sum.inr y)
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
(construct (destruct x)) (construct (destruct y)) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : x = corec (bind.automaton f) (Sum.inr y)
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.in... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | have hβ := congrArg destruct hβ | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : x = corec (bind.automaton f) (Sum.inr y)
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
(construct (destruct x)) (construct (destruct y)) | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : x = corec (bind.automaton f) (Sum.inr y)
hβ : destruct x = destruct (corec (bind.automaton f) (Sum.inr y))
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (S... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : x = corec (bind.automaton f) (Sum.inr y)
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.in... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | clear hβ | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : x = corec (bind.automaton f) (Sum.inr y)
hβ : destruct x = destruct (corec (bind.automaton f) (Sum.inr y))
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (S... | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : destruct x = destruct (corec (bind.automaton f) (Sum.inr y))
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
(construct (destruct x)) (const... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : x = corec (bind.automaton f) (Sum.inr y)
hβ : destruct x = destruct (corec (bind.automaton f) (Sum.inr y))
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y))... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | rw [destruct_corec] at hβ | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : destruct x = destruct (corec (bind.automaton f) (Sum.inr y))
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
(construct (destruct x)) (const... | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : destruct x = Map (corec (bind.automaton f)) (bind.automaton f (Sum.inr y))
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
(construct (destr... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : destruct x = destruct (corec (bind.automaton f) (Sum.inr y))
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | cases hy: destruct y with
| Pure r =>
simp only [Map, hy, bind.automaton] at hβ
rw [hβ]
apply equivF.Pure
rfl
| Free n k =>
simp only [Map, bind.automaton, hy] at hβ
rw [hβ]
apply equivF.Free
intro y
left
rfl | case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : destruct x = Map (corec (bind.automaton f)) (bind.automaton f (Sum.inr y))
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
(construct (destr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : destruct x = Map (corec (bind.automaton f)) (bind.automaton f (Sum.inr y))
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | simp only [Map, hy, bind.automaton] at hβ | case a.Pure
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : destruct x = Map (corec (bind.automaton f)) (bind.automaton f (Sum.inr y))
r : S
hy : destruct y = Functor.Pure r
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.aut... | case a.Pure
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
r : S
hy : destruct y = Functor.Pure r
hβ : destruct x = Functor.Pure r
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
(construct (destruct... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.Pure
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : destruct x = Map (corec (bind.automaton f)) (bind.automaton f (Sum.inr y))
r : S
hy : destruct y = Functor.Pure r
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | rw [hβ] | case a.Pure
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
r : S
hy : destruct y = Functor.Pure r
hβ : destruct x = Functor.Pure r
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
(construct (destruct... | case a.Pure
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
r : S
hy : destruct y = Functor.Pure r
hβ : destruct x = Functor.Pure r
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
(construct (Functor.... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.Pure
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
r : S
hy : destruct y = Functor.Pure r
hβ : destruct x = Functor.Pure r
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = c... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | apply equivF.Pure | case a.Pure
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
r : S
hy : destruct y = Functor.Pure r
hβ : destruct x = Functor.Pure r
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = corec (bind.automaton f) (Sum.inr y))
(construct (Functor.... | case a.Pure.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
r : S
hy : destruct y = Functor.Pure r
hβ : destruct x = Functor.Pure r
β’ r = r | Please generate a tactic in lean4 to solve the state.
STATE:
case a.Pure
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
r : S
hy : destruct y = Functor.Pure r
hβ : destruct x = Functor.Pure r
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequiv Eq fun x y => x = c... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | rfl | case a.Pure.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
r : S
hy : destruct y = Functor.Pure r
hβ : destruct x = Functor.Pure r
β’ r = r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.Pure.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
r : S
hy : destruct y = Functor.Pure r
hβ : destruct x = Functor.Pure r
β’ r = r
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | simp only [Map, bind.automaton, hy] at hβ | case a.Free
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : destruct x = Map (corec (bind.automaton f)) (bind.automaton f (Sum.inr y))
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
β’ equivF Eq
((fun x y => x = corec (bind.automaton f) (Sum.inr y)) β
pequi... | case a.Free
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.inr x =>
match destruct x with
| Functo... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.Free
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
hβ : destruct x = Map (corec (bind.automaton f)) (bind.automaton f (Sum.inr y))
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
β’ equivF Eq
((fun x... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | rw [hβ] | case a.Free
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.inr x =>
match destruct x with
| Functo... | case a.Free
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.inr x =>
match destruct x with
| Functo... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.Free
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.in... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | apply equivF.Free | case a.Free
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.inr x =>
match destruct x with
| Functo... | case a.Free.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.inr x =>
match destruct x with
| Func... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.Free
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.in... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | intro y | case a.Free.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.inr x =>
match destruct x with
| Func... | case a.Free.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x yβ : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct yβ = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.inr x =>
match destruct x with
| Fu... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.Free.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x y : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct y = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | left | case a.Free.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x yβ : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct yβ = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.inr x =>
match destruct x with
| Fu... | case a.Free.a.h
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x yβ : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct yβ = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.inr x =>
match destruct x with
| ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.Free.a
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x yβ : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct yβ = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Su... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_inr | [199, 1] | [228, 6] | rfl | case a.Free.a.h
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x yβ : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct yβ = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| Sum.inr x =>
match destruct x with
| ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.Free.a.h
C : _root_.Container
R S : Type uβ
f : R β Free C S
xβ x yβ : Free C S
n : C.A
k : Container.B C n β Free C S
hy : destruct yβ = Functor.Free n k
hβ :
destruct x =
Functor.Free n
((corec fun x =>
match x with
| ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_pure | [230, 1] | [251, 20] | rw [βconstruct_destruct <| k r] | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ bind (pure r) k = k r | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ bind (pure r) k = construct (destruct (k r)) | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ bind (pure r) k = k r
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_pure | [230, 1] | [251, 20] | rw [βconstruct_destruct <| bind (pure r) k] | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ bind (pure r) k = construct (destruct (k r)) | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ construct (destruct (bind (pure r) k)) = construct (destruct (k r)) | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ bind (pure r) k = construct (destruct (k r))
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_pure | [230, 1] | [251, 20] | simp only [bind, pure, destruct_corec] | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ construct (destruct (bind (pure r) k)) = construct (destruct (k r)) | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ construct (Map (corec (bind.automaton k)) (bind.automaton k (Sum.inl (construct (Functor.Pure r))))) =
construct (destruct (k r)) | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ construct (destruct (bind (pure r) k)) = construct (destruct (k r))
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_pure | [230, 1] | [251, 20] | apply congrArg construct | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ construct (Map (corec (bind.automaton k)) (bind.automaton k (Sum.inl (construct (Functor.Pure r))))) =
construct (destruct (k r)) | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ Map (corec (bind.automaton k)) (bind.automaton k (Sum.inl (construct (Functor.Pure r)))) = destruct (k r) | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ construct (Map (corec (bind.automaton k)) (bind.automaton k (Sum.inl (construct (Functor.Pure r))))) =
construct (destruct (k r))
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_pure | [230, 1] | [251, 20] | conv =>
lhs
congr
. rfl
. simp only [bind.automaton, destruct_construct] | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ Map (corec (bind.automaton k)) (bind.automaton k (Sum.inl (construct (Functor.Pure r)))) = destruct (k r) | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ Map (corec (bind.automaton k)) (Map Sum.inr (destruct (k r))) = destruct (k r) | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ Map (corec (bind.automaton k)) (bind.automaton k (Sum.inl (construct (Functor.Pure r)))) = destruct (k r)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_pure | [230, 1] | [251, 20] | cases destruct (k r) with
| Pure r =>
simp only [Map]
| Free n k =>
simp only [Map]
conv =>
lhs
congr
simp only [Function.comp]
intro x
rw [bind_inr] | C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ Map (corec (bind.automaton k)) (Map Sum.inr (destruct (k r))) = destruct (k r) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : _root_.Container
R S : Type uβ
r : R
k : R β Free C S
β’ Map (corec (bind.automaton k)) (Map Sum.inr (destruct (k r))) = destruct (k r)
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_pure | [230, 1] | [251, 20] | simp only [Map] | case Pure
C : _root_.Container
R S : Type uβ
rβ : R
k : R β Free C S
r : S
β’ Map (corec (bind.automaton k)) (Map Sum.inr (Functor.Pure r)) = Functor.Pure r | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Pure
C : _root_.Container
R S : Type uβ
rβ : R
k : R β Free C S
r : S
β’ Map (corec (bind.automaton k)) (Map Sum.inr (Functor.Pure r)) = Functor.Pure r
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_pure | [230, 1] | [251, 20] | simp only [Map] | case Free
C : _root_.Container
R S : Type uβ
r : R
kβ : R β Free C S
n : C.A
k : Container.B C n β Free C S
β’ Map (corec (bind.automaton kβ)) (Map Sum.inr (Functor.Free n k)) = Functor.Free n k | case Free
C : _root_.Container
R S : Type uβ
r : R
kβ : R β Free C S
n : C.A
k : Container.B C n β Free C S
β’ Functor.Free n (corec (bind.automaton kβ) β Sum.inr β k) = Functor.Free n k | Please generate a tactic in lean4 to solve the state.
STATE:
case Free
C : _root_.Container
R S : Type uβ
r : R
kβ : R β Free C S
n : C.A
k : Container.B C n β Free C S
β’ Map (corec (bind.automaton kβ)) (Map Sum.inr (Functor.Free n k)) = Functor.Free n k
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/FreeMonads.lean | Free.bind_pure | [230, 1] | [251, 20] | conv =>
lhs
congr
simp only [Function.comp]
intro x
rw [bind_inr] | case Free
C : _root_.Container
R S : Type uβ
r : R
kβ : R β Free C S
n : C.A
k : Container.B C n β Free C S
β’ Functor.Free n (corec (bind.automaton kβ) β Sum.inr β k) = Functor.Free n k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Free
C : _root_.Container
R S : Type uβ
r : R
kβ : R β Free C S
n : C.A
k : Container.B C n β Free C S
β’ Functor.Free n (corec (bind.automaton kβ) β Sum.inr β k) = Functor.Free n k
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.wf_destruct | [72, 1] | [79, 10] | simp only [WellFormed, PWellFormed] at wf | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : WellFormed i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wf }).fst),
WellFormed (Next C (Container.M.destruct β{ val := m, property := wf }).fst x)
(PSigma.snd (Container.M.destruct β{ val := m, property := w... | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wf }).fst),
WellFormed (Next C (Container.M.destruct β{ val := m, property := wf }).fst x)
(PSigma.snd (Container.M.destruct β{ val := m... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : WellFormed i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wf }).fst),
WellFormed (Next C (Container.M.destruct β{ val := m, property := wf }).fst x)
... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.wf_destruct | [72, 1] | [79, 10] | rw [βpgfp.unfold] at wf | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wf }).fst),
WellFormed (Next C (Container.M.destruct β{ val := m, property := wf }).fst x)
(PSigma.snd (Container.M.destruct β{ val := m... | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wfβ }).fst),
WellFormed (Next C (Container.M.destruct β{ val := m, property := wfβ ... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wf }).fst),
WellFormed (Next C (Container.M.destruct β{ val := m, property := wf ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.wf_destruct | [72, 1] | [79, 10] | simp only [CompleteLattice.bot_sup] at wf | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wfβ }).fst),
WellFormed (Next C (Container.M.destruct β{ val := m, property := wfβ ... | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wfβ }).fst),
WellFormed (Next C (Container.M.destruct β{ val := m, property := wfβ }).f... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wfβ }).fst),
WellForme... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.wf_destruct | [72, 1] | [79, 10] | have β¨_, yβ© := wf | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wfβ }).fst),
WellFormed (Next C (Container.M.destruct β{ val := m, property := wfβ }).f... | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
leftβ : Idx C (Container.M.destruct m).fst = i
y :
β (x : B C (Container.M.destruct m).fst),
β(pgfp (WellFormedF C)) β₯ (Next C (Container.M.destr... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ β (x : B C (Container.M.destruct β{ val := m, property := wfβ }).fst),
WellFormed (N... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.wf_destruct | [72, 1] | [79, 10] | exact y | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
leftβ : Idx C (Container.M.destruct m).fst = i
y :
β (x : B C (Container.M.destruct m).fst),
β(pgfp (WellFormedF C)) β₯ (Next C (Container.M.destr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
leftβ : Idx C (Container.M.destruct m).fst = i
y :
β (x : B C (Container.M.destruct m).f... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.index_destruct | [81, 1] | [88, 10] | simp only [WellFormed, PWellFormed] at wf | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : WellFormed i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wf }).fst | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wf }).fst | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : WellFormed i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wf }).fst
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.index_destruct | [81, 1] | [88, 10] | rw [βpgfp.unfold] at wf | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wf }).fst | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wfβ }).fst | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wf }).fst
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.index_destruct | [81, 1] | [88, 10] | simp only [CompleteLattice.bot_sup] at wf | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wfβ }).fst | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wfβ }).fst | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wfβ }).fst
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.index_destruct | [81, 1] | [88, 10] | have β¨x, _β© := wf | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wfβ }).fst | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : Idx C (Container.M.destruct m).fst = i
rightβ :
β (x : B C (Container.M.destruct m).fst),
β(pgfp (WellFormedF C)) β₯ (Next C (Container.M.dest... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ i = Idx C (Container.M.destruct β{ val := m, property := wfβ }).fst
TACTIC:
|
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.index_destruct | [81, 1] | [88, 10] | apply Eq.symm | I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : Idx C (Container.M.destruct m).fst = i
rightβ :
β (x : B C (Container.M.destruct m).fst),
β(pgfp (WellFormedF C)) β₯ (Next C (Container.M.dest... | case h
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : Idx C (Container.M.destruct m).fst = i
rightβ :
β (x : B C (Container.M.destruct m).fst),
β(pgfp (WellFormedF C)) β₯ (Next C (Container... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : Idx C (Container.M.destruct m).fst = i
rightβ :
β (x : B C (Container.M.destruct m).... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.index_destruct | [81, 1] | [88, 10] | exact x | case h
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : Idx C (Container.M.destruct m).fst = i
rightβ :
β (x : B C (Container.M.destruct m).fst),
β(pgfp (WellFormedF C)) β₯ (Next C (Container... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
I : Type uβ
C : IContainer' I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
x : Idx C (Container.M.destruct m).fst = i
rightβ :
β (x : B C (Container.M.destr... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | intro β¨x, wfxβ© β¨y, wfyβ© hβ | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
β’ β (x y : M C i), R i x y ... | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toContaine... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | suffices h: x = y by
induction h
rfl | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toContaine... | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toContaine... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | apply Container.M.bisim (Ξ» x y => β i, β (wfx: WellFormed i x) (wfy:WellFormed i y), R i β¨x, wfxβ© β¨y, wfyβ©) | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toContaine... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (to... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | . intro x y β¨i, wfx, wfy, rβ©
have β¨β¨node, hββ©, kβ, kβ, hβ, hβ, hββ© := hβ i β¨x, wfxβ© β¨y, wfyβ© r
have hβ := lift_destruct_eq _ _ _ _ hβ
have hβ := lift_destruct_eq _ _ _ _ hβ
have wfx' := wf_destruct β¨x, wfxβ©
have wfy' := wf_destruct β¨y, wfyβ©
exists node
exists Ξ» a => (kβ a).1
exists Ξ» x => (kβ x).1
sim... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (to... | case a
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toC... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | exists i | case a
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toC... | case a
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toC... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | exists wfx | case a
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toC... | case a
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toC... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | exists wfy | case a
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toC... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), ... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | induction h | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (toContaine... | case refl
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | rfl | case refl
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refl
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | intro x y β¨i, wfx, wfy, rβ© | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
i : I
x : Container.M (to... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | have β¨β¨node, hββ©, kβ, kβ, hβ, hβ, hββ© := hβ i β¨x, wfxβ© β¨y, wfyβ© r | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | have hβ := lift_destruct_eq _ _ _ _ hβ | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | have hβ := lift_destruct_eq _ _ _ _ hβ | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | have wfx' := wf_destruct β¨x, wfxβ© | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | have wfy' := wf_destruct β¨y, wfyβ© | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | exists node | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | exists Ξ» a => (kβ a).1 | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | exists Ξ» x => (kβ x).1 | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | simp only [hβ, hβ, true_and] | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | intro a | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | exists C.Next node a | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | simp only [toContainer] at a | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | exists (by
rw [hβ] at wfx'
apply wfx'
) | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | exists (by
rw [hβ] at wfy'
apply wfy'
) | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | exact hβ a | case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hβ
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode),... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | rw [hβ] at wfx' | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toContai... | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toContai... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | apply wfx' | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toContai... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | rw [hβ] at wfy' | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toContai... | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toContai... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/Test.lean | IContainer'.M.bisim | [139, 1] | [176, 13] | apply wfy' | I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next C (βnode) z) (kβ z) (kβ z)
iβ : I
xβ : Container.M (toContai... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer' I
R : (i : I) β M C i β M C i β Prop
hβ :
β (i : I) (x y : M C i),
R i x y β
β node kβ kβ,
destruct x = { fst := node, snd := kβ } β§
destruct y = { fst := node, snd := kβ } β§ β (z : B C βnode), R (Next... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.wf_destruct | [50, 1] | [57, 10] | simp only [WellFormed, PWellFormed] at wf | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : WellFormed i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wf }).fst.fst
(Container.M.destruct β{ val := m, property := wf }).fst.snd),
WellFormed
(N C (Container.M.destruct β{ val := m, proper... | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wf }).fst.fst
(Container.M.destruct β{ val := m, property := wf }).fst.snd),
WellFormed
(N C (Container.M.destruct β{ v... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : WellFormed i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wf }).fst.fst
(Container.M.destruct β{ val := m, property := wf }).fst.snd),
We... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.wf_destruct | [50, 1] | [57, 10] | rw [βpgfp.unfold] at wf | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wf }).fst.fst
(Container.M.destruct β{ val := m, property := wf }).fst.snd),
WellFormed
(N C (Container.M.destruct β{ v... | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wfβ }).fst.fst
(Container.M.destruct β{ val := m, property := wfβ }).f... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wf }).fst.fst
(Container.M.destruct β{ val := m, property := wf }).f... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.wf_destruct | [50, 1] | [57, 10] | simp only [CompleteLattice.bot_sup] at wf | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wfβ }).fst.fst
(Container.M.destruct β{ val := m, property := wfβ }).f... | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wfβ }).fst.fst
(Container.M.destruct β{ val := m, property := wfβ }).fst.s... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β₯ β β(pgfp (WellFormedF C)) β₯) i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wfβ }).fst.fst
... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.wf_destruct | [50, 1] | [57, 10] | have β¨_, yβ© := wf | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wfβ }).fst.fst
(Container.M.destruct β{ val := m, property := wfβ }).fst.s... | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
leftβ : (Container.M.destruct m).fst.fst = i
y :
β (x : B C (Container.M.destruct m).fst.fst (Container.M.destruct m).fst.snd),
β(pgfp (WellFormed... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
β’ β
(x :
B C (Container.M.destruct β{ val := m, property := wfβ }).fst.fst
... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.wf_destruct | [50, 1] | [57, 10] | exact y | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
leftβ : (Container.M.destruct m).fst.fst = i
y :
β (x : B C (Container.M.destruct m).fst.fst (Container.M.destruct m).fst.snd),
β(pgfp (WellFormed... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wfβ : β(pgfp (WellFormedF C)) β₯ i m
wf : β(WellFormedF C) (β(pgfp (WellFormedF C)) β₯) i m
leftβ : (Container.M.destruct m).fst.fst = i
y :
β (x : B C (Container.M.destruct m).fst.... |
https://github.com/RemyCiterin/LeanCoInd.git | 69d305ae769624f460f9c1ee6a0351917f4b74cf | CoInd/MIdx.lean | IContainer.M.index_destruct | [59, 1] | [66, 10] | simp only [WellFormed, PWellFormed] at wf | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : WellFormed i m
β’ i = (Container.M.destruct β{ val := m, property := wf }).fst.fst | I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : β(pgfp (WellFormedF C)) β₯ i m
β’ i = (Container.M.destruct β{ val := m, property := wf }).fst.fst | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type uβ
C : IContainer I
i : I
xβ : M C i
m : Container.M (toContainer C)
wf : WellFormed i m
β’ i = (Container.M.destruct β{ val := m, property := wf }).fst.fst
TACTIC:
|
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