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/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | by_cases c1 : y β binders | case a.h.e'_3.a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binde... | case pos
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v =... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_3.a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | left | case pos
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v =... | case pos.h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | exact c1 | case pos.h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | right | case neg
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v =... | case neg.h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [h3 y c1] | case neg.h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | case neg.h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | exact h1_right c1 | case neg.h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | congr! 1 | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case a.h.e'_1.a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binde... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | exact phi_ih V V' Ο Ο' binders h1 h2 h2' h3 | case a.h.e'_1.a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binde... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | cases h1 | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case intro
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | congr! 1 | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case a.h.e'_1.a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binde... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | exact phi_ih V V' Ο Ο' binders h1_left h2 h2' h3 | case a.h.e'_1.a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binde... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | exact psi_ih V V' Ο Ο' binders h1_right h2 h2' h3 | case a.h.e'_2.a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binde... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2.a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | first | apply forall_congr' | apply exists_congr | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | intro d | case h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο... | case h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | apply phi_ih (Function.updateITE V x d) (Function.updateITE V' x d) Ο (Function.updateITE Ο' x x) (binders βͺ {x}) h1 | case h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο... | case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | apply forall_congr' | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | apply exists_congr | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case h
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | intro v a1 | case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [Function.updateITE] at a1 | case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp at a1 | case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [Function.updateITE] | case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | split_ifs | case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | case pos
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v =... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | case _ c1 c2 =>
rfl | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | case _ c1 c2 =>
contradiction | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | case _ c1 c2 =>
subst c2
tauto | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | case _ c1 c2 =>
simp only [if_neg c1] at a1
apply h2
tauto | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | rfl | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | contradiction | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | subst c2 | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | tauto | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [if_neg c1] at a1 | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | apply h2 | D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β bind... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | tauto | case a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | intro v a1 | case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp at a1 | case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [Function.updateITE] | case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | split_ifs <;> tauto | case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2'
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | intro v a1 | case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp at a1 | case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [Function.updateITE] | case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | split_ifs <;> tauto | case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h3
D : Type
I : Interpretation D
headβ : Definition
tailβ : List Definition
tail_ihβ :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | split_ifs | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | case pos
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | case _ c1 c2 =>
simp only [List.length_map] at c2
contradiction | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | case _ c1 c2 =>
simp at c2
contradiction | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | case _ c1 c2 =>
specialize ih V V' Ο Ο' binders (def_ X xs)
simp only [fastReplaceFree] at ih
apply ih h1 h2 h2' h3 | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | have s1 : List.map V xs = List.map (V' β Ο') xs | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [s1] | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | apply Holds_coincide_Var | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | case h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | intro v a1 | case h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | apply Function.updateListITE_mem_eq_len | case h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case h1.h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [List.map_eq_map_iff] | case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | intro x a1 | case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp | case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | apply h2 | case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case s1.a
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | by_cases c3 : x β binders | case s1.a
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case pos
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1.a
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binder... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | left | case pos
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case pos.h
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | exact c3 | case pos.h
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | right | case neg
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case neg.h
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [h3 x c3] | case neg.h
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case neg.h
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | exact h1 x a1 c3 | case neg.h
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [isFreeIn_iff_mem_freeVarSet] at a1 | case h1.h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case h1.h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [β List.mem_toFinset] | case h1.h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case h1.h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | apply Finset.mem_of_subset hd.h1 a1 | case h1.h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp | case h1.h2
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | case h1.h2
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | tauto | case h1.h2
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [List.length_map] at c2 | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | contradiction | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp at c2 | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | contradiction | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | specialize ih V V' Ο Ο' binders (def_ X xs) | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)) β
(β v β binders, v = Ο' v) β
(β... | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
X : DefName
xs : List VarName
V V' : VarAssignment D
Ο Ο' : VarName β VarName
binders : Finset VarName
h1 : β v β xs, v β binders β Ο v β binders
h2 : β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)
h2' : β v β binders, v = Ο' v
h3 : β v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
ih :
β (V V' : VarAssignment D) (Ο Ο' : VarName β VarName) (binders : Finset VarName) (F : Formula),
admitsAux Ο binders F β
(β (v : VarName), v β binders β¨ Ο' v β binders β V v = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | simp only [fastReplaceFree] at ih | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
X : DefName
xs : List VarName
V V' : VarAssignment D
Ο Ο' : VarName β VarName
binders : Finset VarName
h1 : β v β xs, v β binders β Ο v β binders
h2 : β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)
h2' : β v β binders, v = Ο' v
h3 : β v... | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
X : DefName
xs : List VarName
V V' : VarAssignment D
Ο Ο' : VarName β VarName
binders : Finset VarName
h1 : β v β xs, v β binders β Ο v β binders
h2 : β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)
h2' : β v β binders, v = Ο' v
h3 : β v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
X : DefName
xs : List VarName
V V' : VarAssignment D
Ο Ο' : VarName β VarName
binders : Finset VarName
h1 : β v β xs, v β binders β Ο v β binders
h2 : β (v : VarName), v β binders β¨ Ο' v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem_aux | [74, 1] | [207, 28] | apply ih h1 h2 h2' h3 | D : Type
I : Interpretation D
hd : Definition
tl : List Definition
X : DefName
xs : List VarName
V V' : VarAssignment D
Ο Ο' : VarName β VarName
binders : Finset VarName
h1 : β v β xs, v β binders β Ο v β binders
h2 : β (v : VarName), v β binders β¨ Ο' v β binders β V v = V' (Ο' v)
h2' : β v β binders, v = Ο' v
h3 : β v... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
hd : Definition
tl : List Definition
X : DefName
xs : List VarName
V V' : VarAssignment D
Ο Ο' : VarName β VarName
binders : Finset VarName
h1 : β v β xs, v β binders β Ο v β binders
h2 : β (v : VarName), v β binders β¨ Ο' v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem | [210, 1] | [224, 9] | apply substitution_theorem_aux D I (V β Ο) V E Ο Ο β
F h1 | D : Type
I : Interpretation D
V : VarAssignment D
E : Env
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
β’ Holds D I (V β Ο) E F β Holds D I V E (fastReplaceFree Ο F) | case h2
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
β’ β (v : VarName), v β β
β¨ Ο v β β
β (V β Ο) v = V (Ο v)
case h2'
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
β’ β v β β
, v = Ο v
case h3
D... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
β’ Holds D I (V β Ο) E F β Holds D I V E (fastReplaceFree Ο F)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem | [210, 1] | [224, 9] | simp | case h2
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
β’ β (v : VarName), v β β
β¨ Ο v β β
β (V β Ο) v = V (Ο v) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
β’ β (v : VarName), v β β
β¨ Ο v β β
β (V β Ο) v = V (Ο v)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem | [210, 1] | [224, 9] | simp | case h2'
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
β’ β v β β
, v = Ο v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2'
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
β’ β v β β
, v = Ο v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_theorem | [210, 1] | [224, 9] | simp | case h3
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
β’ β v β β
, Ο v = Ο v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h3
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
β’ β v β β
, Ο v = Ο v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_is_valid | [227, 1] | [239, 25] | simp only [IsValid] at h2 | Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : F.IsValid
β’ (fastReplaceFree Ο F).IsValid | Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ (fastReplaceFree Ο F).IsValid | Please generate a tactic in lean4 to solve the state.
STATE:
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : F.IsValid
β’ (fastReplaceFree Ο F).IsValid
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_is_valid | [227, 1] | [239, 25] | simp only [IsValid] | Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ (fastReplaceFree Ο F).IsValid | Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E (fastReplaceFree Ο F) | Please generate a tactic in lean4 to solve the state.
STATE:
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ (fastReplaceFree Ο F).IsValid
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_is_valid | [227, 1] | [239, 25] | intro D I V E | Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E (fastReplaceFree Ο F) | Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
β’ Holds D I V E (fastReplaceFree Ο F) | Please generate a tactic in lean4 to solve the state.
STATE:
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E (fastReplaceFree Ο F)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_is_valid | [227, 1] | [239, 25] | simp only [β substitution_theorem D I V E Ο F h1] | Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
β’ Holds D I V E (fastReplaceFree Ο F) | Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
β’ Holds D I (V β Ο) E F | Please generate a tactic in lean4 to solve the state.
STATE:
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
β’ Holds D I V E (fastReplaceFree Ο F)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Rec/Admits.lean | FOL.NV.Sub.Var.All.Rec.substitution_is_valid | [227, 1] | [239, 25] | exact h2 D I (V β Ο) E | Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
β’ Holds D I (V β Ο) E F | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ο : VarName β VarName
F : Formula
h1 : admits Ο F
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
β’ Holds D I (V β Ο) E F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_cons_to_set_union | [9, 1] | [17, 9] | ext a | Ξ± : Type
inst : DecidableEq Ξ±
ys : List Ξ±
x : Ξ±
β’ β(x :: ys).toFinset = {x} βͺ βys.toFinset | case h
Ξ± : Type
inst : DecidableEq Ξ±
ys : List Ξ±
x a : Ξ±
β’ a β β(x :: ys).toFinset β a β {x} βͺ βys.toFinset | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
inst : DecidableEq Ξ±
ys : List Ξ±
x : Ξ±
β’ β(x :: ys).toFinset = {x} βͺ βys.toFinset
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_cons_to_set_union | [9, 1] | [17, 9] | simp | case h
Ξ± : Type
inst : DecidableEq Ξ±
ys : List Ξ±
x a : Ξ±
β’ a β β(x :: ys).toFinset β a β {x} βͺ βys.toFinset | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
Ξ± : Type
inst : DecidableEq Ξ±
ys : List Ξ±
x a : Ξ±
β’ a β β(x :: ys).toFinset β a β {x} βͺ βys.toFinset
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_append_to_set_union | [19, 1] | [26, 9] | ext a | Ξ± : Type
inst : DecidableEq Ξ±
xs ys : List Ξ±
β’ β(xs ++ ys).toFinset = βxs.toFinset βͺ βys.toFinset | case h
Ξ± : Type
inst : DecidableEq Ξ±
xs ys : List Ξ±
a : Ξ±
β’ a β β(xs ++ ys).toFinset β a β βxs.toFinset βͺ βys.toFinset | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
inst : DecidableEq Ξ±
xs ys : List Ξ±
β’ β(xs ++ ys).toFinset = βxs.toFinset βͺ βys.toFinset
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_append_to_set_union | [19, 1] | [26, 9] | simp | case h
Ξ± : Type
inst : DecidableEq Ξ±
xs ys : List Ξ±
a : Ξ±
β’ a β β(xs ++ ys).toFinset β a β βxs.toFinset βͺ βys.toFinset | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
Ξ± : Type
inst : DecidableEq Ξ±
xs ys : List Ξ±
a : Ξ±
β’ a β β(xs ++ ys).toFinset β a β βxs.toFinset βͺ βys.toFinset
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | induction g | Node : Type
instβ : DecidableEq Node
g : Graph Node
β’ β (x y : Node), y β direct_succ_list g x β β ys, y β ys β§ (x, ys) β g | case nil
Node : Type
instβ : DecidableEq Node
β’ β (x y : Node), y β direct_succ_list [] x β β ys, y β ys β§ (x, ys) β []
case cons
Node : Type
instβ : DecidableEq Node
headβ : Node Γ List Node
tailβ : List (Node Γ List Node)
tail_ihβ : β (x y : Node), y β direct_succ_list tailβ x β β ys, y β ys β§ (x, ys) β tailβ
β’ β (x... | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
g : Graph Node
β’ β (x y : Node), y β direct_succ_list g x β β ys, y β ys β§ (x, ys) β g
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | case nil =>
simp only [direct_succ_list]
simp | Node : Type
instβ : DecidableEq Node
β’ β (x y : Node), y β direct_succ_list [] x β β ys, y β ys β§ (x, ys) β [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
β’ β (x y : Node), y β direct_succ_list [] x β β ys, y β ys β§ (x, ys) β []
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | simp only [direct_succ_list] | Node : Type
instβ : DecidableEq Node
β’ β (x y : Node), y β direct_succ_list [] x β β ys, y β ys β§ (x, ys) β [] | Node : Type
instβ : DecidableEq Node
β’ β (x y : Node), y β [] β β ys, y β ys β§ (x, ys) β [] | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
β’ β (x y : Node), y β direct_succ_list [] x β β ys, y β ys β§ (x, ys) β []
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | simp | Node : Type
instβ : DecidableEq Node
β’ β (x y : Node), y β [] β β ys, y β ys β§ (x, ys) β [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
β’ β (x y : Node), y β [] β β ys, y β ys β§ (x, ys) β []
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | simp only [direct_succ_list] | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
β’ β (x y : Node), y β direct_succ_list (hd :: tl) x β β ys, y β ys β§ (x, ys) β hd :: tl | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
β’ β (x y : Node),
(y β if hd.1 = x then hd.2 ++ direct_succ_list tl x else direct_succ_list tl x) β β ys, y β ys β§ (x, ys) β hd :: tl | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
β’ β (x y : Node), y β direct_succ_list (hd :: tl) x β β ys, y β ys β§ (x, ys) β hd :: tl
TACTIC... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | intro x y | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
β’ β (x y : Node),
(y β if hd.1 = x then hd.2 ++ direct_succ_list tl x else direct_succ_list tl x) β β ys, y β ys β§ (x, ys) β hd :: tl | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
β’ (y β if hd.1 = x then hd.2 ++ direct_succ_list tl x else direct_succ_list tl x) β β ys, y β ys β§ (x, ys) β hd :: tl | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
β’ β (x y : Node),
(y β if hd.1 = x then hd.2 ++ direct_succ_list tl x else direct_succ_lis... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | split_ifs | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
β’ (y β if hd.1 = x then hd.2 ++ direct_succ_list tl x else direct_succ_list tl x) β β ys, y β ys β§ (x, ys) β hd :: tl | case pos
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
hβ : hd.1 = x
β’ y β hd.2 ++ direct_succ_list tl x β β ys, y β ys β§ (x, ys) β hd :: tl
case neg
Node : Type
instβ : DecidableEq Node
hd... | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
β’ (y β if hd.1 = x then hd.2 ++ direct_succ_list tl x else direct_succ_list tl x) β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | subst c1 | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : hd.1 = x
β’ y β hd.2 ++ direct_succ_list tl x β β ys, y β ys β§ (x, ys) β hd :: tl | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ y β hd.2 ++ direct_succ_list tl hd.1 β β ys, y β ys β§ (hd.1, ys) β hd :: tl | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : hd.1 = x
β’ y β hd.2 ++ direct_succ_list tl x β β ys, y β ys β§ (x, ys) β hd :: ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | simp | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ y β hd.2 ++ direct_succ_list tl hd.1 β β ys, y β ys β§ (hd.1, ys) β hd :: tl | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ y β hd.2 β¨ y β direct_succ_list tl hd.1 β β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ y β hd.2 ++ direct_succ_list tl hd.1 β β ys, y β ys β§ (hd.1, ys) β hd :: tl
TACTIC:... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | simp only [ih] | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ y β hd.2 β¨ y β direct_succ_list tl hd.1 β β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ (y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl) β β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ y β hd.2 β¨ y β direct_succ_list tl hd.1 β β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | constructor | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ (y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl) β β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ (y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl) β β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl)
case mpr
Node : Type
instβ : Decidable... | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ (y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl) β β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | intro a1 | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ (y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl) β β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl
β’ β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ (y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl) β β ys, y β ys β§ ((hd.1, ys) = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | cases a1 | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl
β’ β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | case mp.inl
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
hβ : y β hd.2
β’ β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl)
case mp.inr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl
β’ β ys, y β ys β§ ((hd.1, ys) =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | case _ left =>
apply Exists.intro hd.snd
tauto | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
left : y β hd.2
β’ β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
left : y β hd.2
β’ β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl)
TACTIC:
|
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