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/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.replaceFreeAux_admitsAux | [853, 1] | [905, 10] | tauto | case exists_
v t a✝¹ : VarName
a✝ : Formula
a_ih✝ : ∀ (binders : Finset VarName), ¬occursIn t a✝ → admitsAux t v binders (replaceFreeAux v t binders a✝)
binders : Finset VarName
h1 : ¬(t = a✝¹ ∨ occursIn t a✝)
⊢ admitsAux t v (binders ∪ {a✝¹}) (replaceFreeAux v t (binders ∪ {a✝¹}) a✝) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case exists_
v t a✝¹ : VarName
a✝ : Formula
a_ih✝ : ∀ (binders : Finset VarName), ¬occursIn t a✝ → admitsAux t v binders (replaceFreeAux v t binders a✝)
binders : Finset VarName
h1 : ¬(t = a✝¹ ∨ occursIn t a✝)
⊢ admitsAux t v (binders ∪ {a✝¹}) (replaceFreeAux... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.replaceFree_admits | [908, 1] | [916, 44] | simp only [replaceFree] | F : Formula
v t : VarName
h1 : ¬occursIn t F
⊢ admits t v (replaceFree v t F) | F : Formula
v t : VarName
h1 : ¬occursIn t F
⊢ admits t v (replaceFreeAux v t ∅ F) | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v t : VarName
h1 : ¬occursIn t F
⊢ admits t v (replaceFree v t F)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.replaceFree_admits | [908, 1] | [916, 44] | simp only [admits] | F : Formula
v t : VarName
h1 : ¬occursIn t F
⊢ admits t v (replaceFreeAux v t ∅ F) | F : Formula
v t : VarName
h1 : ¬occursIn t F
⊢ admitsAux t v ∅ (replaceFreeAux v t ∅ F) | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v t : VarName
h1 : ¬occursIn t F
⊢ admits t v (replaceFreeAux v t ∅ F)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.replaceFree_admits | [908, 1] | [916, 44] | exact replaceFreeAux_admitsAux F v t ∅ h1 | F : Formula
v t : VarName
h1 : ¬occursIn t F
⊢ admitsAux t v ∅ (replaceFreeAux v t ∅ F) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v t : VarName
h1 : ¬occursIn t F
⊢ admitsAux t v ∅ (replaceFreeAux v t ∅ F)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | induction F generalizing S | F : Formula
v u : VarName
S T : Finset VarName
h1 : admitsAux v u S F
h2 : u ∉ T
⊢ admitsAux v u (S ∪ T) F | case pred_const_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : admitsAux v u S (pred_const_ a✝¹ a✝)
⊢ admitsAux v u (S ∪ T) (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : adm... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
S T : Finset VarName
h1 : admitsAux v u S F
h2 : u ∉ T
⊢ admitsAux v u (S ∪ T) F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | all_goals
simp only [admitsAux] at h1
simp only [admitsAux] | case pred_const_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : admitsAux v u S (pred_const_ a✝¹ a✝)
⊢ admitsAux v u (S ∪ T) (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : adm... | case pred_const_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S → u ∉ S
⊢ v ∈ a✝ ∧ v ∉ S ∪ T → u ∉ S ∪ T
case pred_var_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S → u ∉ S
⊢ v ∈ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : admitsAux v u S (pred_const_ a✝¹ a✝)
⊢ admitsAux v u (S ∪ T) (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
T : Finset VarName
h2 : u ∉ T... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | case pred_const_ X xs | pred_var_ X xs | eq_ x y |def_ X xs =>
simp
tauto | v u : VarName
T : Finset VarName
h2 : u ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S → u ∉ S
⊢ v ∈ xs ∧ v ∉ S ∪ T → u ∉ S ∪ T | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : u ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S → u ∉ S
⊢ v ∈ xs ∧ v ∉ S ∪ T → u ∉ S ∪ T
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | case forall_ x phi phi_ih | exists_ x phi phi_ih =>
simp only [Finset.union_right_comm S T {x}]
tauto | v u : VarName
T : Finset VarName
h2 : u ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u S phi → admitsAux v u (S ∪ T) phi
S : Finset VarName
h1 : admitsAux v u (S ∪ {x}) phi
⊢ admitsAux v u (S ∪ T ∪ {x}) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : u ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u S phi → admitsAux v u (S ∪ T) phi
S : Finset VarName
h1 : admitsAux v u (S ∪ {x}) phi
⊢ admitsAux v u (S ∪ T ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | all_goals
tauto | case not_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝ : Formula
a_ih✝ : ∀ (S : Finset VarName), admitsAux v u S a✝ → admitsAux v u (S ∪ T) a✝
S : Finset VarName
h1 : admitsAux v u S a✝
⊢ admitsAux v u (S ∪ T) a✝
case imp_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ a✝ : Formula
a_ih✝¹ : ∀ (S : Finset VarName), ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case not_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝ : Formula
a_ih✝ : ∀ (S : Finset VarName), admitsAux v u S a✝ → admitsAux v u (S ∪ T) a✝
S : Finset VarName
h1 : admitsAux v u S a✝
⊢ admitsAux v u (S ∪ T) a✝
case imp_
v u : VarName
T : Finset VarName
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | simp only [admitsAux] at h1 | case def_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : admitsAux v u S (def_ a✝¹ a✝)
⊢ admitsAux v u (S ∪ T) (def_ a✝¹ a✝) | case def_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S → u ∉ S
⊢ admitsAux v u (S ∪ T) (def_ a✝¹ a✝) | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : admitsAux v u S (def_ a✝¹ a✝)
⊢ admitsAux v u (S ∪ T) (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | simp only [admitsAux] | case def_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S → u ∉ S
⊢ admitsAux v u (S ∪ T) (def_ a✝¹ a✝) | case def_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S → u ∉ S
⊢ v ∈ a✝ ∧ v ∉ S ∪ T → u ∉ S ∪ T | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S → u ∉ S
⊢ admitsAux v u (S ∪ T) (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | simp | v u : VarName
T : Finset VarName
h2 : u ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S → u ∉ S
⊢ v ∈ xs ∧ v ∉ S ∪ T → u ∉ S ∪ T | v u : VarName
T : Finset VarName
h2 : u ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S → u ∉ S
⊢ v ∈ xs → v ∉ S → v ∉ T → u ∉ S ∧ u ∉ T | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : u ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S → u ∉ S
⊢ v ∈ xs ∧ v ∉ S ∪ T → u ∉ S ∪ T
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | tauto | v u : VarName
T : Finset VarName
h2 : u ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S → u ∉ S
⊢ v ∈ xs → v ∉ S → v ∉ T → u ∉ S ∧ u ∉ T | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : u ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S → u ∉ S
⊢ v ∈ xs → v ∉ S → v ∉ T → u ∉ S ∧ u ∉ T
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | simp only [Finset.union_right_comm S T {x}] | v u : VarName
T : Finset VarName
h2 : u ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u S phi → admitsAux v u (S ∪ T) phi
S : Finset VarName
h1 : admitsAux v u (S ∪ {x}) phi
⊢ admitsAux v u (S ∪ T ∪ {x}) phi | v u : VarName
T : Finset VarName
h2 : u ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u S phi → admitsAux v u (S ∪ T) phi
S : Finset VarName
h1 : admitsAux v u (S ∪ {x}) phi
⊢ admitsAux v u (S ∪ {x} ∪ T) phi | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : u ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u S phi → admitsAux v u (S ∪ T) phi
S : Finset VarName
h1 : admitsAux v u (S ∪ {x}) phi
⊢ admitsAux v u (S ∪ T ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | tauto | v u : VarName
T : Finset VarName
h2 : u ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u S phi → admitsAux v u (S ∪ T) phi
S : Finset VarName
h1 : admitsAux v u (S ∪ {x}) phi
⊢ admitsAux v u (S ∪ {x} ∪ T) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : u ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u S phi → admitsAux v u (S ∪ T) phi
S : Finset VarName
h1 : admitsAux v u (S ∪ {x}) phi
⊢ admitsAux v u (S ∪ {x} ∪ T) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_add_binders | [920, 1] | [940, 10] | tauto | case iff_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ a✝ : Formula
a_ih✝¹ : ∀ (S : Finset VarName), admitsAux v u S a✝¹ → admitsAux v u (S ∪ T) a✝¹
a_ih✝ : ∀ (S : Finset VarName), admitsAux v u S a✝ → admitsAux v u (S ∪ T) a✝
S : Finset VarName
h1 : admitsAux v u S a✝¹ ∧ admitsAux v u S a✝
⊢ admitsAux v u (S ∪ T) a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case iff_
v u : VarName
T : Finset VarName
h2 : u ∉ T
a✝¹ a✝ : Formula
a_ih✝¹ : ∀ (S : Finset VarName), admitsAux v u S a✝¹ → admitsAux v u (S ∪ T) a✝¹
a_ih✝ : ∀ (S : Finset VarName), admitsAux v u S a✝ → admitsAux v u (S ∪ T) a✝
S : Finset VarName
h1 : admit... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | induction F generalizing S | F : Formula
v u : VarName
S T : Finset VarName
h1 : admitsAux v u (S ∪ T) F
h2 : v ∉ T
⊢ admitsAux v u S F | case pred_const_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : admitsAux v u (S ∪ T) (pred_const_ a✝¹ a✝)
⊢ admitsAux v u S (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : adm... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
S T : Finset VarName
h1 : admitsAux v u (S ∪ T) F
h2 : v ∉ T
⊢ admitsAux v u S F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | all_goals
simp only [admitsAux] at h1
simp only [admitsAux] | case pred_const_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : admitsAux v u (S ∪ T) (pred_const_ a✝¹ a✝)
⊢ admitsAux v u S (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : adm... | case pred_const_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S ∪ T → u ∉ S ∪ T
⊢ v ∈ a✝ ∧ v ∉ S → u ∉ S
case pred_var_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S ∪ T → u ∉ S ∪ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : PredName
a✝ : List VarName
S : Finset VarName
h1 : admitsAux v u (S ∪ T) (pred_const_ a✝¹ a✝)
⊢ admitsAux v u S (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
T : Finset VarName
h2 : v ∉ T... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | case pred_const_ X xs | pred_var_ X xs | eq_ x y | def_ X xs =>
simp at h1
tauto | v u : VarName
T : Finset VarName
h2 : v ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S ∪ T → u ∉ S ∪ T
⊢ v ∈ xs ∧ v ∉ S → u ∉ S | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : v ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S ∪ T → u ∉ S ∪ T
⊢ v ∈ xs ∧ v ∉ S → u ∉ S
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | case not_ phi phi_ih =>
exact phi_ih S h1 | v u : VarName
T : Finset VarName
h2 : v ∉ T
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ T) phi
⊢ admitsAux v u S phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : v ∉ T
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ T) phi
⊢ admitsAux v u S phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | case
imp_ phi psi phi_ih psi_ih
| and_ phi psi phi_ih psi_ih
| or_ phi psi phi_ih psi_ih
| iff_ phi psi phi_ih psi_ih =>
tauto | v u : VarName
T : Finset VarName
h2 : v ∉ T
phi psi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
psi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) psi → admitsAux v u S psi
S : Finset VarName
h1 : admitsAux v u (S ∪ T) phi ∧ admitsAux v u (S ∪ T) psi
⊢ admitsAux v u S ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : v ∉ T
phi psi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
psi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) psi → admitsAux v u S psi
S : Finset VarName
h1 : admitsAux v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | case forall_ x phi phi_ih | exists_ x phi phi_ih =>
simp only [Finset.union_right_comm S T {x}] at h1
tauto | v u : VarName
T : Finset VarName
h2 : v ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ T ∪ {x}) phi
⊢ admitsAux v u (S ∪ {x}) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : v ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ T ∪ {x}) phi
⊢ admitsAux v u (S ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | simp only [admitsAux] at h1 | case def_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : admitsAux v u (S ∪ T) (def_ a✝¹ a✝)
⊢ admitsAux v u S (def_ a✝¹ a✝) | case def_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S ∪ T → u ∉ S ∪ T
⊢ admitsAux v u S (def_ a✝¹ a✝) | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : admitsAux v u (S ∪ T) (def_ a✝¹ a✝)
⊢ admitsAux v u S (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | simp only [admitsAux] | case def_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S ∪ T → u ∉ S ∪ T
⊢ admitsAux v u S (def_ a✝¹ a✝) | case def_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S ∪ T → u ∉ S ∪ T
⊢ v ∈ a✝ ∧ v ∉ S → u ∉ S | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
T : Finset VarName
h2 : v ∉ T
a✝¹ : DefName
a✝ : List VarName
S : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ S ∪ T → u ∉ S ∪ T
⊢ admitsAux v u S (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | simp at h1 | v u : VarName
T : Finset VarName
h2 : v ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S ∪ T → u ∉ S ∪ T
⊢ v ∈ xs ∧ v ∉ S → u ∉ S | v u : VarName
T : Finset VarName
h2 : v ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs → v ∉ S → v ∉ T → u ∉ S ∧ u ∉ T
⊢ v ∈ xs ∧ v ∉ S → u ∉ S | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : v ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs ∧ v ∉ S ∪ T → u ∉ S ∪ T
⊢ v ∈ xs ∧ v ∉ S → u ∉ S
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | tauto | v u : VarName
T : Finset VarName
h2 : v ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs → v ∉ S → v ∉ T → u ∉ S ∧ u ∉ T
⊢ v ∈ xs ∧ v ∉ S → u ∉ S | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : v ∉ T
X : DefName
xs : List VarName
S : Finset VarName
h1 : v ∈ xs → v ∉ S → v ∉ T → u ∉ S ∧ u ∉ T
⊢ v ∈ xs ∧ v ∉ S → u ∉ S
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | exact phi_ih S h1 | v u : VarName
T : Finset VarName
h2 : v ∉ T
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ T) phi
⊢ admitsAux v u S phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : v ∉ T
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ T) phi
⊢ admitsAux v u S phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | tauto | v u : VarName
T : Finset VarName
h2 : v ∉ T
phi psi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
psi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) psi → admitsAux v u S psi
S : Finset VarName
h1 : admitsAux v u (S ∪ T) phi ∧ admitsAux v u (S ∪ T) psi
⊢ admitsAux v u S ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : v ∉ T
phi psi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
psi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) psi → admitsAux v u S psi
S : Finset VarName
h1 : admitsAux v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | simp only [Finset.union_right_comm S T {x}] at h1 | v u : VarName
T : Finset VarName
h2 : v ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ T ∪ {x}) phi
⊢ admitsAux v u (S ∪ {x}) phi | v u : VarName
T : Finset VarName
h2 : v ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ {x} ∪ T) phi
⊢ admitsAux v u (S ∪ {x}) phi | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : v ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ T ∪ {x}) phi
⊢ admitsAux v u (S ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_del_binders | [943, 1] | [971, 10] | tauto | v u : VarName
T : Finset VarName
h2 : v ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ {x} ∪ T) phi
⊢ admitsAux v u (S ∪ {x}) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u : VarName
T : Finset VarName
h2 : v ∉ T
x : VarName
phi : Formula
phi_ih : ∀ (S : Finset VarName), admitsAux v u (S ∪ T) phi → admitsAux v u S phi
S : Finset VarName
h1 : admitsAux v u (S ∪ {x} ∪ T) phi
⊢ admitsAux v u (S ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | induction F generalizing binders | F : Formula
v u : VarName
binders : Finset VarName
h1 : admitsAux v u binders F
h2 : isFreeIn v F
h3 : v ∉ binders
⊢ u ∉ binders | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : admitsAux v u binders (pred_const_ a✝¹ a✝)
h2 : isFreeIn v (pred_const_ a✝¹ a✝)
h3 : v ∉ binders
⊢ u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : admitsAux v u binders ... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
binders : Finset VarName
h1 : admitsAux v u binders F
h2 : isFreeIn v F
h3 : v ∉ binders
⊢ u ∉ binders
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | all_goals
simp only [admitsAux] at h1
simp only [isFreeIn] at h2 | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : admitsAux v u binders (pred_const_ a✝¹ a✝)
h2 : isFreeIn v (pred_const_ a✝¹ a✝)
h3 : v ∉ binders
⊢ u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : admitsAux v u binders ... | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : v ∈ a✝
h3 : v ∉ binders
⊢ u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : v ∈ a✝
h3 : v ∉... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : admitsAux v u binders (pred_const_ a✝¹ a✝)
h2 : isFreeIn v (pred_const_ a✝¹ a✝)
h3 : v ∉ binders
⊢ u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | all_goals
tauto | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : v ∈ a✝
h3 : v ∉ binders
⊢ u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : v ∈ a✝
h3 : v ∉... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : v ∈ a✝
h3 : v ∉ binders
⊢ u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | simp only [admitsAux] at h1 | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : admitsAux v u binders (def_ a✝¹ a✝)
h2 : isFreeIn v (def_ a✝¹ a✝)
h3 : v ∉ binders
⊢ u ∉ binders | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : isFreeIn v (def_ a✝¹ a✝)
h3 : v ∉ binders
⊢ u ∉ binders | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : admitsAux v u binders (def_ a✝¹ a✝)
h2 : isFreeIn v (def_ a✝¹ a✝)
h3 : v ∉ binders
⊢ u ∉ binders
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | simp only [isFreeIn] at h2 | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : isFreeIn v (def_ a✝¹ a✝)
h3 : v ∉ binders
⊢ u ∉ binders | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : v ∈ a✝
h3 : v ∉ binders
⊢ u ∉ binders | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : isFreeIn v (def_ a✝¹ a✝)
h3 : v ∉ binders
⊢ u ∉ binders
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | cases h2 | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h2 : ¬v = x ∧ isFreeIn v phi
h3 : v ∉ binders
⊢ u ∉ binders | case intro
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
left✝ : ¬v = x
right✝ : isFreeIn v phi
⊢ u ∉ binders | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h2 : ¬v = x ∧ isFreeIn v phi
h3 : v ∉ binders
⊢ u ∉ bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | apply phi_ih binders | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : isFreeIn v phi
⊢ u ∉ binders | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : isFreeIn v phi
⊢ admitsAux v u binders phi
case h2
v u x : Var... | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : isFreeIn v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | apply admitsAux_del_binders phi v u binders {x} h1 | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : isFreeIn v phi
⊢ admitsAux v u binders phi | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : isFreeIn v phi
⊢ v ∉ {x} | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : is... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | simp | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : isFreeIn v phi
⊢ v ∉ {x} | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : isFreeIn v phi
⊢ ¬v = x | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : is... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | exact h2_left | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : isFreeIn v phi
⊢ ¬v = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : is... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | exact h2_right | case h2
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : isFreeIn v phi
⊢ isFreeIn v phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : is... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | exact h3 | case h3
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : isFreeIn v phi
⊢ v ∉ binders | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h3
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), admitsAux v u binders phi → isFreeIn v phi → v ∉ binders → u ∉ binders
binders : Finset VarName
h1 : admitsAux v u (binders ∪ {x}) phi
h3 : v ∉ binders
h2_left : ¬v = x
h2_right : is... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_isFreeIn | [974, 1] | [998, 10] | tauto | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : v ∈ a✝
h3 : v ∉ binders
⊢ u ∉ binders | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
h2 : v ∈ a✝
h3 : v ∉ binders
⊢ u ∉ binders
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | induction E generalizing F binders V | D : Type
I : Interpretation D
V V' : VarAssignment D
E : Env
v t : VarName
binders : Finset VarName
F : Formula
h1 : fastAdmitsAux v t binders F
h2 : ∀ v ∉ binders, V' v = V v
⊢ Holds D I (Function.updateITE V v (V' t)) E F ↔ Holds D I V E (fastReplaceFree v t F) | case nil
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
V : VarAssignment D
binders : Finset VarName
F : Formula
h1 : fastAdmitsAux v t binders F
h2 : ∀ v ∉ binders, V' v = V v
⊢ Holds D I (Function.updateITE V v (V' t)) [] F ↔ Holds D I V [] (fastReplaceFree v t F)
case cons
D : Type
I : Interpretat... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V V' : VarAssignment D
E : Env
v t : VarName
binders : Finset VarName
F : Formula
h1 : fastAdmitsAux v t binders F
h2 : ∀ v ∉ binders, V' v = V v
⊢ Holds D I (Function.updateITE V v (V' t)) E F ↔ Holds D I V E (fastReplaceFree v ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | induction F generalizing binders V | case cons
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) ta... | case cons.pred_const_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V ... | Please generate a tactic in lean4 to solve the state.
STATE:
case cons
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | all_goals
simp only [fastAdmitsAux] at h1
simp only [fastReplaceFree]
simp only [Holds] | case cons.pred_const_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V ... | case cons.pred_const_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V ... | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.pred_const_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case pred_const_ X xs | pred_var_ X xs =>
simp
congr! 1
simp only [List.map_eq_map_iff]
intro x a1
simp
simp only [Function.updateITE]
split_ifs
case _ c1 c2 =>
subst c1
tauto
case _ c1 c2 =>
subst c1
contradiction
case _ c1 c2 =>
subst c2
contradiction
case _ c1 c2 =>
... | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case eq_ x y =>
simp only [Function.updateITE]
simp only [eq_comm]
congr! 1
all_goals
split_ifs
case _ c1 =>
subst c1
tauto
case _ c1 =>
rfl | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case not_ phi phi_ih =>
congr! 1
exact phi_ih V binders h1 h2 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case forall_ x phi phi_ih | exists_ x phi phi_ih =>
split_ifs
case _ c1 =>
subst c1
simp only [Holds]
first | apply forall_congr' | apply exists_congr
intro d
congr! 1
funext x
simp only [Function.updateITE]
split_ifs <;> rfl
case _ c1 =>
simp only [Holds]
first | apply for... | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp only [fastAdmitsAux] at h1 | case cons.def_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t... | case cons.def_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t... | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.def_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp only [fastReplaceFree] | case cons.def_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t... | case cons.def_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t... | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.def_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp only [Holds] | case cons.def_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t... | case cons.def_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t... | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.def_
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | congr! 1 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp only [List.map_eq_map_iff] | case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | intro x a1 | case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp | case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp only [Function.updateITE] | case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | split_ifs | case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tai... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_4
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case _ c1 c2 =>
subst c1
tauto | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case _ c1 c2 =>
subst c1
contradiction | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case _ c1 c2 =>
subst c2
contradiction | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case _ c1 c2 =>
rfl | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | subst c1 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | D : Type
I : Interpretation D
V' : VarAssignment D
t : VarName
head✝ : Definition
tail✝ : List Definition
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : ∀ v ∉ binders, V' v = V v
x : VarName
a1 : x ∈ xs
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | tauto | D : Type
I : Interpretation D
V' : VarAssignment D
t : VarName
head✝ : Definition
tail✝ : List Definition
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : ∀ v ∉ binders, V' v = V v
x : VarName
a1 : x ∈ xs
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
t : VarName
head✝ : Definition
tail✝ : List Definition
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : ∀ v ∉ binders, V' v = V v
x : VarName
a1 : x ∈ xs
tail_ih✝ :
∀ (V : Va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | subst c1 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | D : Type
I : Interpretation D
V' : VarAssignment D
t : VarName
head✝ : Definition
tail✝ : List Definition
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : ∀ v ∉ binders, V' v = V v
x : VarName
a1 : x ∈ xs
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | contradiction | D : Type
I : Interpretation D
V' : VarAssignment D
t : VarName
head✝ : Definition
tail✝ : List Definition
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : ∀ v ∉ binders, V' v = V v
x : VarName
a1 : x ∈ xs
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
t : VarName
head✝ : Definition
tail✝ : List Definition
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : ∀ v ∉ binders, V' v = V v
x : VarName
a1 : x ∈ xs
tail_ih✝ :
∀ (V : Va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | subst c2 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | contradiction | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | rfl | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp only [Function.updateITE] | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp only [eq_comm] | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | congr! 1 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | case a.h.e'_2
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | all_goals
split_ifs
case _ c1 =>
subst c1
tauto
case _ c1 =>
rfl | case a.h.e'_2
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | split_ifs | case a.h.e'_3
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)... | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tai... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_3
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case _ c1 =>
subst c1
tauto | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case _ c1 =>
rfl | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | subst c1 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | tauto | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | rfl | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | congr! 1 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | exact phi_ih V binders h1 h2 | case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | cases h1 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | case intro
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) t... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | congr! 1 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | exact phi_ih V binders h1_left h2 | case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | exact psi_ih V binders h1_right h2 | case a.h.e'_2.a
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2.a
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | split_ifs | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tai... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case _ c1 =>
subst c1
simp only [Holds]
first | apply forall_congr' | apply exists_congr
intro d
congr! 1
funext x
simp only [Function.updateITE]
split_ifs <;> rfl | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | case _ c1 =>
simp only [Holds]
first | apply forall_congr' | apply exists_congr
intro d
cases h1
case inl h1 =>
contradiction
case inr h1 =>
simp only [Function.updateITE_comm V v x d (V' t) c1]
apply phi_ih (Function.updateITE V x d) (binders ∪ {x}) h1
simp only [Function.updateITE]
sim... | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | subst c1 | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | first | apply forall_congr' | apply exists_congr | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | intro d | case h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | congr! 1 | case h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝... | case h.a.h.e'_3
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | funext x | case h.a.h.e'_3
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' ... | case h.a.h.e'_3.h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a.h.e'_3
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | simp only [Function.updateITE] | case h.a.h.e'_3.h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V... | case h.a.h.e'_3.h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a.h.e'_3.h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | split_ifs <;> rfl | case h.a.h.e'_3.h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a.h.e'_3.h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | apply forall_congr' | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.substitution_theorem_aux | [1001, 1] | [1136, 17] | apply exists_congr | D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Ho... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
(Holds D I (Function.updateITE V v (V' t)) tail✝... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
fastAdmitsAux v t binders F →
(∀ v ∉ binders, V' v = V v) →
... |
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