Datasets:
internlm
/
Lean-Github

Dataset card Data Studio Files Community
1
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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
unfold Formula.metaVarSet at h1
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1 : (phi.imp_ psi).metaVarSet = βˆ… ⊒ sub Οƒ Ο„ (phi.imp_ psi) = sub Οƒ Ο„' (phi.imp_ psi)
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1 : phi.metaVarSet βˆͺ psi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ (phi.imp_ psi) = sub Οƒ Ο„' (phi.imp_ psi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
simp only [Finset.union_eq_empty] at h1
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1 : phi.metaVarSet βˆͺ psi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ (phi.imp_ psi) = sub Οƒ Ο„' (phi.imp_ psi)
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1 : phi.metaVarSet = βˆ… ∧ psi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ (phi.imp_ psi) = sub Οƒ Ο„' (phi.imp_ psi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
unfold sub
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1 : phi.metaVarSet = βˆ… ∧ psi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ (phi.imp_ psi) = sub Οƒ Ο„' (phi.imp_ psi)
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1 : phi.metaVarSet = βˆ… ∧ psi.metaVarSet = βˆ… ⊒ (sub Οƒ Ο„ phi).imp_ (sub Οƒ Ο„ psi) = (sub Οƒ Ο„' phi).imp_ (sub Οƒ Ο„' psi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
cases h1
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1 : phi.metaVarSet = βˆ… ∧ psi.metaVarSet = βˆ… ⊒ (sub Οƒ Ο„ phi).imp_ (sub Οƒ Ο„ psi) = (sub Οƒ Ο„' phi).imp_ (sub Οƒ Ο„' psi)
case intro Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi left✝ : phi.metaVarSet = βˆ… right✝ : psi.metaVarSet = βˆ… ⊒ (sub Οƒ Ο„ phi).imp_ (sub Οƒ Ο„ psi) = (sub Οƒ Ο„' phi).imp_ (sub Οƒ Ο„' psi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
congr! 1
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1_left : phi.metaVarSet = βˆ… h1_right : psi.metaVarSet = βˆ… ⊒ (sub Οƒ Ο„ phi).imp_ (sub Οƒ Ο„ psi) = (sub Οƒ Ο„' phi).imp_ (sub Οƒ Ο„' psi)
case h.e'_1 Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1_left : phi.metaVarSet = βˆ… h1_right : psi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi case h.e'_2 Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1_left : phi.metaVarSet = βˆ… h1_right : psi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
exact phi_ih h1_left
case h.e'_1 Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1_left : phi.metaVarSet = βˆ… h1_right : psi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
exact psi_ih h1_right
case h.e'_2 Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation phi psi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi psi_ih : psi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi h1_left : phi.metaVarSet = βˆ… h1_right : psi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ psi = sub Οƒ Ο„' psi
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
unfold Formula.metaVarSet at h1
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation x : VarName phi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi h1 : (forall_ x phi).metaVarSet = βˆ… ⊒ sub Οƒ Ο„ (forall_ x phi) = sub Οƒ Ο„' (forall_ x phi)
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation x : VarName phi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi h1 : phi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ (forall_ x phi) = sub Οƒ Ο„' (forall_ x phi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
unfold sub
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation x : VarName phi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi h1 : phi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ (forall_ x phi) = sub Οƒ Ο„' (forall_ x phi)
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation x : VarName phi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi h1 : phi.metaVarSet = βˆ… ⊒ forall_ (↑σ x) (sub Οƒ Ο„ phi) = forall_ (↑σ x) (sub Οƒ Ο„' phi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
congr! 1
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation x : VarName phi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi h1 : phi.metaVarSet = βˆ… ⊒ forall_ (↑σ x) (sub Οƒ Ο„ phi) = forall_ (↑σ x) (sub Οƒ Ο„' phi)
case h.e'_2 Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation x : VarName phi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi h1 : phi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
exact phi_ih h1
case h.e'_2 Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation x : VarName phi : Formula phi_ih : phi.metaVarSet = βˆ… β†’ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi h1 : phi.metaVarSet = βˆ… ⊒ sub Οƒ Ο„ phi = sub Οƒ Ο„' phi
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub
[820, 1]
[860, 8]
rfl
Οƒ : Instantiation Ο„ Ο„' : MetaInstantiation X : DefName xs : List VarName h1 : (def_ X xs).metaVarSet = βˆ… ⊒ sub Οƒ Ο„ (def_ X xs) = sub Οƒ Ο„' (def_ X xs)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
induction F generalizing vs
F : Formula vs : List VarName Οƒ : Instantiation Ο„ : MetaInstantiation h1 : NoMetaVarAndAllFreeInList vs F ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ F)
case meta_var_ Οƒ : Instantiation Ο„ : MetaInstantiation a✝ : MetaVarName vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (meta_var_ a✝) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (meta_var_ a✝)) case pred_ Οƒ : Instantiation Ο„ : MetaInstantiation a✝¹ : PredName a✝ vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (pred_ a✝¹ a✝) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (pred_ a✝¹ a✝)) case eq_ Οƒ : Instantiation Ο„ : MetaInstantiation a✝¹ a✝ : VarName vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (eq_ a✝¹ a✝) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (eq_ a✝¹ a✝)) case true_ Οƒ : Instantiation Ο„ : MetaInstantiation vs : List VarName h1 : NoMetaVarAndAllFreeInList vs true_ ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ true_) case not_ Οƒ : Instantiation Ο„ : MetaInstantiation a✝ : Formula a_ih✝ : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs a✝ β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ a✝) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs a✝.not_ ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ a✝.not_) case imp_ Οƒ : Instantiation Ο„ : MetaInstantiation a✝¹ a✝ : Formula a_ih✝¹ : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs a✝¹ β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ a✝¹) a_ih✝ : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs a✝ β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ a✝) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (a✝¹.imp_ a✝) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (a✝¹.imp_ a✝)) case forall_ Οƒ : Instantiation Ο„ : MetaInstantiation a✝¹ : VarName a✝ : Formula a_ih✝ : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs a✝ β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ a✝) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (forall_ a✝¹ a✝) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (forall_ a✝¹ a✝)) case def_ Οƒ : Instantiation Ο„ : MetaInstantiation a✝¹ : DefName a✝ vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (def_ a✝¹ a✝) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (def_ a✝¹ a✝))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
case meta_var_ X => unfold NoMetaVarAndAllFreeInList at h1 contradiction
Οƒ : Instantiation Ο„ : MetaInstantiation X : MetaVarName vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (meta_var_ X) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (meta_var_ X))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
case pred_ X xs => unfold sub unfold NoMetaVarAndAllFreeInList exact List.map_subset Οƒ.1 h1
Οƒ : Instantiation Ο„ : MetaInstantiation X : PredName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (pred_ X xs))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
case true_ => unfold sub unfold NoMetaVarAndAllFreeInList simp
Οƒ : Instantiation Ο„ : MetaInstantiation vs : List VarName h1 : NoMetaVarAndAllFreeInList vs true_ ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ true_)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
case not_ phi phi_ih => unfold NoMetaVarAndAllFreeInList at h1 unfold sub unfold NoMetaVarAndAllFreeInList exact phi_ih vs h1
Οƒ : Instantiation Ο„ : MetaInstantiation phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi.not_ ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi.not_)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
case forall_ x phi phi_ih => unfold NoMetaVarAndAllFreeInList at h1 unfold sub unfold NoMetaVarAndAllFreeInList simp only [← List.map_cons] exact phi_ih (x :: vs) h1
Οƒ : Instantiation Ο„ : MetaInstantiation x : VarName phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (forall_ x phi) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (forall_ x phi))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
case def_ X xs => unfold sub unfold NoMetaVarAndAllFreeInList exact List.map_subset Οƒ.val h1
Οƒ : Instantiation Ο„ : MetaInstantiation X : DefName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (def_ X xs) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (def_ X xs))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList at h1
Οƒ : Instantiation Ο„ : MetaInstantiation X : MetaVarName vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (meta_var_ X) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (meta_var_ X))
Οƒ : Instantiation Ο„ : MetaInstantiation X : MetaVarName vs : List VarName h1 : False ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (meta_var_ X))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
contradiction
Οƒ : Instantiation Ο„ : MetaInstantiation X : MetaVarName vs : List VarName h1 : False ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (meta_var_ X))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold sub
Οƒ : Instantiation Ο„ : MetaInstantiation X : PredName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (pred_ X xs))
Οƒ : Instantiation Ο„ : MetaInstantiation X : PredName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (pred_ X (List.map (↑σ) xs))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList
Οƒ : Instantiation Ο„ : MetaInstantiation X : PredName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (pred_ X (List.map (↑σ) xs))
Οƒ : Instantiation Ο„ : MetaInstantiation X : PredName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs) ⊒ List.map (↑σ) xs βŠ† List.map (↑σ) vs
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
exact List.map_subset Οƒ.1 h1
Οƒ : Instantiation Ο„ : MetaInstantiation X : PredName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs) ⊒ List.map (↑σ) xs βŠ† List.map (↑σ) vs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold sub
Οƒ : Instantiation Ο„ : MetaInstantiation vs : List VarName h1 : NoMetaVarAndAllFreeInList vs true_ ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ true_)
Οƒ : Instantiation Ο„ : MetaInstantiation vs : List VarName h1 : NoMetaVarAndAllFreeInList vs true_ ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) true_
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList
Οƒ : Instantiation Ο„ : MetaInstantiation vs : List VarName h1 : NoMetaVarAndAllFreeInList vs true_ ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) true_
Οƒ : Instantiation Ο„ : MetaInstantiation vs : List VarName h1 : NoMetaVarAndAllFreeInList vs true_ ⊒ True
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
simp
Οƒ : Instantiation Ο„ : MetaInstantiation vs : List VarName h1 : NoMetaVarAndAllFreeInList vs true_ ⊒ True
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList at h1
Οƒ : Instantiation Ο„ : MetaInstantiation phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi.not_ ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi.not_)
Οƒ : Instantiation Ο„ : MetaInstantiation phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi.not_)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold sub
Οƒ : Instantiation Ο„ : MetaInstantiation phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi.not_)
Οƒ : Instantiation Ο„ : MetaInstantiation phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi).not_
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList
Οƒ : Instantiation Ο„ : MetaInstantiation phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi).not_
Οƒ : Instantiation Ο„ : MetaInstantiation phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
exact phi_ih vs h1
Οƒ : Instantiation Ο„ : MetaInstantiation phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList at h1
Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (phi.imp_ psi) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (phi.imp_ psi))
Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ∧ NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (phi.imp_ psi))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold sub
Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ∧ NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (phi.imp_ psi))
Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ∧ NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) ((sub Οƒ Ο„ phi).imp_ (sub Οƒ Ο„ psi))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList
Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ∧ NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) ((sub Οƒ Ο„ phi).imp_ (sub Οƒ Ο„ psi))
Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ∧ NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) ∧ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
cases h1
Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs phi ∧ NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) ∧ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi)
case intro Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName left✝ : NoMetaVarAndAllFreeInList vs phi right✝ : NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) ∧ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
constructor
Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1_left : NoMetaVarAndAllFreeInList vs phi h1_right : NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) ∧ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi)
case left Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1_left : NoMetaVarAndAllFreeInList vs phi h1_right : NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) case right Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1_left : NoMetaVarAndAllFreeInList vs phi h1_right : NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
exact phi_ih vs h1_left
case left Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1_left : NoMetaVarAndAllFreeInList vs phi h1_right : NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
exact psi_ih vs h1_right
case right Οƒ : Instantiation Ο„ : MetaInstantiation phi psi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) psi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi) vs : List VarName h1_left : NoMetaVarAndAllFreeInList vs phi h1_right : NoMetaVarAndAllFreeInList vs psi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ psi)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList at h1
Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (eq_ x y) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (eq_ x y))
Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1 : x ∈ vs ∧ y ∈ vs ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (eq_ x y))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold sub
Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1 : x ∈ vs ∧ y ∈ vs ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (eq_ x y))
Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1 : x ∈ vs ∧ y ∈ vs ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (eq_ (↑σ x) (↑σ y))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList
Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1 : x ∈ vs ∧ y ∈ vs ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (eq_ (↑σ x) (↑σ y))
Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1 : x ∈ vs ∧ y ∈ vs ⊒ ↑σ x ∈ List.map (↑σ) vs ∧ ↑σ y ∈ List.map (↑σ) vs
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
cases h1
Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1 : x ∈ vs ∧ y ∈ vs ⊒ ↑σ x ∈ List.map (↑σ) vs ∧ ↑σ y ∈ List.map (↑σ) vs
case intro Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName left✝ : x ∈ vs right✝ : y ∈ vs ⊒ ↑σ x ∈ List.map (↑σ) vs ∧ ↑σ y ∈ List.map (↑σ) vs
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
constructor
Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1_left : x ∈ vs h1_right : y ∈ vs ⊒ ↑σ x ∈ List.map (↑σ) vs ∧ ↑σ y ∈ List.map (↑σ) vs
case left Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1_left : x ∈ vs h1_right : y ∈ vs ⊒ ↑σ x ∈ List.map (↑σ) vs case right Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1_left : x ∈ vs h1_right : y ∈ vs ⊒ ↑σ y ∈ List.map (↑σ) vs
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
exact List.mem_map_of_mem Οƒ.val h1_left
case left Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1_left : x ∈ vs h1_right : y ∈ vs ⊒ ↑σ x ∈ List.map (↑σ) vs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
exact List.mem_map_of_mem Οƒ.val h1_right
case right Οƒ : Instantiation Ο„ : MetaInstantiation x y : VarName vs : List VarName h1_left : x ∈ vs h1_right : y ∈ vs ⊒ ↑σ y ∈ List.map (↑σ) vs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList at h1
Οƒ : Instantiation Ο„ : MetaInstantiation x : VarName phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (forall_ x phi) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (forall_ x phi))
Οƒ : Instantiation Ο„ : MetaInstantiation x : VarName phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList (x :: vs) phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (forall_ x phi))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold sub
Οƒ : Instantiation Ο„ : MetaInstantiation x : VarName phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList (x :: vs) phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (forall_ x phi))
Οƒ : Instantiation Ο„ : MetaInstantiation x : VarName phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList (x :: vs) phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (forall_ (↑σ x) (sub Οƒ Ο„ phi))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList
Οƒ : Instantiation Ο„ : MetaInstantiation x : VarName phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList (x :: vs) phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (forall_ (↑σ x) (sub Οƒ Ο„ phi))
Οƒ : Instantiation Ο„ : MetaInstantiation x : VarName phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList (x :: vs) phi ⊒ NoMetaVarAndAllFreeInList (↑σ x :: List.map (↑σ) vs) (sub Οƒ Ο„ phi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
simp only [← List.map_cons]
Οƒ : Instantiation Ο„ : MetaInstantiation x : VarName phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList (x :: vs) phi ⊒ NoMetaVarAndAllFreeInList (↑σ x :: List.map (↑σ) vs) (sub Οƒ Ο„ phi)
Οƒ : Instantiation Ο„ : MetaInstantiation x : VarName phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList (x :: vs) phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) (x :: vs)) (sub Οƒ Ο„ phi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
exact phi_ih (x :: vs) h1
Οƒ : Instantiation Ο„ : MetaInstantiation x : VarName phi : Formula phi_ih : βˆ€ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β†’ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ phi) vs : List VarName h1 : NoMetaVarAndAllFreeInList (x :: vs) phi ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) (x :: vs)) (sub Οƒ Ο„ phi)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold sub
Οƒ : Instantiation Ο„ : MetaInstantiation X : DefName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (def_ X xs) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub Οƒ Ο„ (def_ X xs))
Οƒ : Instantiation Ο„ : MetaInstantiation X : DefName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (def_ X xs) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (def_ X (List.map (↑σ) xs))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
unfold NoMetaVarAndAllFreeInList
Οƒ : Instantiation Ο„ : MetaInstantiation X : DefName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (def_ X xs) ⊒ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (def_ X (List.map (↑σ) xs))
Οƒ : Instantiation Ο„ : MetaInstantiation X : DefName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (def_ X xs) ⊒ List.map (↑σ) xs βŠ† List.map (↑σ) vs
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.no_meta_var_and_all_free_in_list_map_sub
[863, 1]
[920, 35]
exact List.map_subset Οƒ.val h1
Οƒ : Instantiation Ο„ : MetaInstantiation X : DefName xs vs : List VarName h1 : NoMetaVarAndAllFreeInList vs (def_ X xs) ⊒ List.map (↑σ) xs βŠ† List.map (↑σ) vs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
induction F
F : Formula E : Env Οƒ : Instantiation h1 : IsMetaVarOrAllDefInEnv E F ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ F)
case meta_var_ E : Env Οƒ : Instantiation a✝ : MetaVarName h1 : IsMetaVarOrAllDefInEnv E (meta_var_ a✝) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (meta_var_ a✝)) case pred_ E : Env Οƒ : Instantiation a✝¹ : PredName a✝ : List VarName h1 : IsMetaVarOrAllDefInEnv E (pred_ a✝¹ a✝) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (pred_ a✝¹ a✝)) case eq_ E : Env Οƒ : Instantiation a✝¹ a✝ : VarName h1 : IsMetaVarOrAllDefInEnv E (eq_ a✝¹ a✝) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (eq_ a✝¹ a✝)) case true_ E : Env Οƒ : Instantiation h1 : IsMetaVarOrAllDefInEnv E true_ ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ true_) case not_ E : Env Οƒ : Instantiation a✝ : Formula a_ih✝ : IsMetaVarOrAllDefInEnv E a✝ β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ a✝) h1 : IsMetaVarOrAllDefInEnv E a✝.not_ ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ a✝.not_) case imp_ E : Env Οƒ : Instantiation a✝¹ a✝ : Formula a_ih✝¹ : IsMetaVarOrAllDefInEnv E a✝¹ β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ a✝¹) a_ih✝ : IsMetaVarOrAllDefInEnv E a✝ β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ a✝) h1 : IsMetaVarOrAllDefInEnv E (a✝¹.imp_ a✝) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (a✝¹.imp_ a✝)) case forall_ E : Env Οƒ : Instantiation a✝¹ : VarName a✝ : Formula a_ih✝ : IsMetaVarOrAllDefInEnv E a✝ β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ a✝) h1 : IsMetaVarOrAllDefInEnv E (forall_ a✝¹ a✝) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (forall_ a✝¹ a✝)) case def_ E : Env Οƒ : Instantiation a✝¹ : DefName a✝ : List VarName h1 : IsMetaVarOrAllDefInEnv E (def_ a✝¹ a✝) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (def_ a✝¹ a✝))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
case meta_var_ X => unfold sub unfold IsMetaVarOrAllDefInEnv simp only
E : Env Οƒ : Instantiation X : MetaVarName h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (meta_var_ X))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
case pred_ X xs => unfold sub unfold IsMetaVarOrAllDefInEnv simp only
E : Env Οƒ : Instantiation X : PredName xs : List VarName h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (pred_ X xs))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
case eq_ x y => unfold sub unfold IsMetaVarOrAllDefInEnv simp only
E : Env Οƒ : Instantiation x y : VarName h1 : IsMetaVarOrAllDefInEnv E (eq_ x y) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (eq_ x y))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
case true_ => unfold sub unfold IsMetaVarOrAllDefInEnv simp only
E : Env Οƒ : Instantiation h1 : IsMetaVarOrAllDefInEnv E true_ ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ true_)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
case not_ phi phi_ih => unfold IsMetaVarOrAllDefInEnv at h1 unfold sub unfold IsMetaVarOrAllDefInEnv exact phi_ih h1
E : Env Οƒ : Instantiation phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi.not_ ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi.not_)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
case forall_ x phi phi_ih => unfold IsMetaVarOrAllDefInEnv at h1 unfold sub unfold IsMetaVarOrAllDefInEnv exact phi_ih h1
E : Env Οƒ : Instantiation x : VarName phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E (forall_ x phi) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (forall_ x phi))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
case def_ X xs => unfold IsMetaVarOrAllDefInEnv at h1 unfold sub unfold IsMetaVarOrAllDefInEnv simp exact h1
E : Env Οƒ : Instantiation X : DefName xs : List VarName h1 : IsMetaVarOrAllDefInEnv E (def_ X xs) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (def_ X xs))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold sub
E : Env Οƒ : Instantiation X : MetaVarName h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (meta_var_ X))
E : Env Οƒ : Instantiation X : MetaVarName h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X) ⊒ IsMetaVarOrAllDefInEnv E (meta_var_ X)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv
E : Env Οƒ : Instantiation X : MetaVarName h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X) ⊒ IsMetaVarOrAllDefInEnv E (meta_var_ X)
E : Env Οƒ : Instantiation X : MetaVarName h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X) ⊒ True
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
simp only
E : Env Οƒ : Instantiation X : MetaVarName h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X) ⊒ True
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold sub
E : Env Οƒ : Instantiation X : PredName xs : List VarName h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (pred_ X xs))
E : Env Οƒ : Instantiation X : PredName xs : List VarName h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs) ⊒ IsMetaVarOrAllDefInEnv E (pred_ X (List.map (↑σ) xs))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv
E : Env Οƒ : Instantiation X : PredName xs : List VarName h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs) ⊒ IsMetaVarOrAllDefInEnv E (pred_ X (List.map (↑σ) xs))
E : Env Οƒ : Instantiation X : PredName xs : List VarName h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs) ⊒ True
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
simp only
E : Env Οƒ : Instantiation X : PredName xs : List VarName h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs) ⊒ True
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold sub
E : Env Οƒ : Instantiation x y : VarName h1 : IsMetaVarOrAllDefInEnv E (eq_ x y) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (eq_ x y))
E : Env Οƒ : Instantiation x y : VarName h1 : IsMetaVarOrAllDefInEnv E (eq_ x y) ⊒ IsMetaVarOrAllDefInEnv E (eq_ (↑σ x) (↑σ y))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv
E : Env Οƒ : Instantiation x y : VarName h1 : IsMetaVarOrAllDefInEnv E (eq_ x y) ⊒ IsMetaVarOrAllDefInEnv E (eq_ (↑σ x) (↑σ y))
E : Env Οƒ : Instantiation x y : VarName h1 : IsMetaVarOrAllDefInEnv E (eq_ x y) ⊒ True
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
simp only
E : Env Οƒ : Instantiation x y : VarName h1 : IsMetaVarOrAllDefInEnv E (eq_ x y) ⊒ True
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold sub
E : Env Οƒ : Instantiation h1 : IsMetaVarOrAllDefInEnv E true_ ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ true_)
E : Env Οƒ : Instantiation h1 : IsMetaVarOrAllDefInEnv E true_ ⊒ IsMetaVarOrAllDefInEnv E true_
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv
E : Env Οƒ : Instantiation h1 : IsMetaVarOrAllDefInEnv E true_ ⊒ IsMetaVarOrAllDefInEnv E true_
E : Env Οƒ : Instantiation h1 : IsMetaVarOrAllDefInEnv E true_ ⊒ True
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
simp only
E : Env Οƒ : Instantiation h1 : IsMetaVarOrAllDefInEnv E true_ ⊒ True
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv at h1
E : Env Οƒ : Instantiation phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi.not_ ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi.not_)
E : Env Οƒ : Instantiation phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi.not_)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold sub
E : Env Οƒ : Instantiation phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi.not_)
E : Env Οƒ : Instantiation phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi).not_
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv
E : Env Οƒ : Instantiation phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi).not_
E : Env Οƒ : Instantiation phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
exact phi_ih h1
E : Env Οƒ : Instantiation phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv at h1
E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1 : IsMetaVarOrAllDefInEnv E (phi.imp_ psi) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (phi.imp_ psi))
E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (phi.imp_ psi))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold sub
E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (phi.imp_ psi))
E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E ((sub Οƒ meta_var_ phi).imp_ (sub Οƒ meta_var_ psi))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv
E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E ((sub Οƒ meta_var_ phi).imp_ (sub Οƒ meta_var_ psi))
E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) ∧ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
cases h1
E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) ∧ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi)
case intro E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) left✝ : IsMetaVarOrAllDefInEnv E phi right✝ : IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) ∧ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
constructor
E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1_left : IsMetaVarOrAllDefInEnv E phi h1_right : IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) ∧ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi)
case left E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1_left : IsMetaVarOrAllDefInEnv E phi h1_right : IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) case right E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1_left : IsMetaVarOrAllDefInEnv E phi h1_right : IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
exact phi_ih h1_left
case left E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1_left : IsMetaVarOrAllDefInEnv E phi h1_right : IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
exact psi_ih h1_right
case right E : Env Οƒ : Instantiation phi psi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) psi_ih : IsMetaVarOrAllDefInEnv E psi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi) h1_left : IsMetaVarOrAllDefInEnv E phi h1_right : IsMetaVarOrAllDefInEnv E psi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ psi)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv at h1
E : Env Οƒ : Instantiation x : VarName phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E (forall_ x phi) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (forall_ x phi))
E : Env Οƒ : Instantiation x : VarName phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (forall_ x phi))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold sub
E : Env Οƒ : Instantiation x : VarName phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (forall_ x phi))
E : Env Οƒ : Instantiation x : VarName phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (forall_ (↑σ x) (sub Οƒ meta_var_ phi))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv
E : Env Οƒ : Instantiation x : VarName phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (forall_ (↑σ x) (sub Οƒ meta_var_ phi))
E : Env Οƒ : Instantiation x : VarName phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
exact phi_ih h1
E : Env Οƒ : Instantiation x : VarName phi : Formula phi_ih : IsMetaVarOrAllDefInEnv E phi β†’ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi) h1 : IsMetaVarOrAllDefInEnv E phi ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ phi)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv at h1
E : Env Οƒ : Instantiation X : DefName xs : List VarName h1 : IsMetaVarOrAllDefInEnv E (def_ X xs) ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (def_ X xs))
E : Env Οƒ : Instantiation X : DefName xs : List VarName h1 : βˆƒ d ∈ E, X = d.name ∧ xs.length = d.args.length ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (def_ X xs))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold sub
E : Env Οƒ : Instantiation X : DefName xs : List VarName h1 : βˆƒ d ∈ E, X = d.name ∧ xs.length = d.args.length ⊒ IsMetaVarOrAllDefInEnv E (sub Οƒ meta_var_ (def_ X xs))
E : Env Οƒ : Instantiation X : DefName xs : List VarName h1 : βˆƒ d ∈ E, X = d.name ∧ xs.length = d.args.length ⊒ IsMetaVarOrAllDefInEnv E (def_ X (List.map (↑σ) xs))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
unfold IsMetaVarOrAllDefInEnv
E : Env Οƒ : Instantiation X : DefName xs : List VarName h1 : βˆƒ d ∈ E, X = d.name ∧ xs.length = d.args.length ⊒ IsMetaVarOrAllDefInEnv E (def_ X (List.map (↑σ) xs))
E : Env Οƒ : Instantiation X : DefName xs : List VarName h1 : βˆƒ d ∈ E, X = d.name ∧ xs.length = d.args.length ⊒ βˆƒ d ∈ E, X = d.name ∧ (List.map (↑σ) xs).length = d.args.length
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
simp
E : Env Οƒ : Instantiation X : DefName xs : List VarName h1 : βˆƒ d ∈ E, X = d.name ∧ xs.length = d.args.length ⊒ βˆƒ d ∈ E, X = d.name ∧ (List.map (↑σ) xs).length = d.args.length
E : Env Οƒ : Instantiation X : DefName xs : List VarName h1 : βˆƒ d ∈ E, X = d.name ∧ xs.length = d.args.length ⊒ βˆƒ d ∈ E, X = d.name ∧ xs.length = d.args.length
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.sub_meta_id_preserves_is_meta_var_or_all_def_in_env
[923, 1]
[975, 13]
exact h1
E : Env Οƒ : Instantiation X : DefName xs : List VarName h1 : βˆƒ d ∈ E, X = d.name ∧ xs.length = d.args.length ⊒ βˆƒ d ∈ E, X = d.name ∧ xs.length = d.args.length
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.well_formed_env_has_no_dup
[978, 1]
[1000, 34]
induction E
E : Env h1 : E.WellFormed ⊒ E.Nodup
case nil h1 : Env.WellFormed [] ⊒ Env.Nodup [] case cons head✝ : Definition tail✝ : List Definition tail_ih✝ : Env.WellFormed tail✝ β†’ Env.Nodup tail✝ h1 : Env.WellFormed (head✝ :: tail✝) ⊒ Env.Nodup (head✝ :: tail✝)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.well_formed_env_has_no_dup
[978, 1]
[1000, 34]
case nil => unfold Env.Nodup simp
h1 : Env.WellFormed [] ⊒ Env.Nodup []
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.well_formed_env_has_no_dup
[978, 1]
[1000, 34]
unfold Env.Nodup
h1 : Env.WellFormed [] ⊒ Env.Nodup []
h1 : Env.WellFormed [] ⊒ List.Pairwise (fun d1 d2 => d1.name = d2.name β†’ d1.args.length = d2.args.length β†’ False) []
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.well_formed_env_has_no_dup
[978, 1]
[1000, 34]
simp
h1 : Env.WellFormed [] ⊒ List.Pairwise (fun d1 d2 => d1.name = d2.name β†’ d1.args.length = d2.args.length β†’ False) []
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.well_formed_env_has_no_dup
[978, 1]
[1000, 34]
unfold Env.Nodup at ih
hd : Definition tl : List Definition ih : Env.WellFormed tl β†’ Env.Nodup tl h1 : Env.WellFormed (hd :: tl) ⊒ Env.Nodup (hd :: tl)
hd : Definition tl : List Definition ih : Env.WellFormed tl β†’ List.Pairwise (fun d1 d2 => d1.name = d2.name β†’ d1.args.length = d2.args.length β†’ False) tl h1 : Env.WellFormed (hd :: tl) ⊒ Env.Nodup (hd :: tl)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.well_formed_env_has_no_dup
[978, 1]
[1000, 34]
unfold Env.WellFormed at h1
hd : Definition tl : List Definition ih : Env.WellFormed tl β†’ List.Pairwise (fun d1 d2 => d1.name = d2.name β†’ d1.args.length = d2.args.length β†’ False) tl h1 : Env.WellFormed (hd :: tl) ⊒ Env.Nodup (hd :: tl)
hd : Definition tl : List Definition ih : Env.WellFormed tl β†’ List.Pairwise (fun d1 d2 => d1.name = d2.name β†’ d1.args.length = d2.args.length β†’ False) tl h1 : (βˆ€ d' ∈ tl, hd.name = d'.name β†’ hd.args.length = d'.args.length β†’ False) ∧ IsMetaVarOrAllDefInEnv tl hd.F ∧ Env.WellFormed tl ⊒ Env.Nodup (hd :: tl)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/MM0/MM0.lean
MM0.well_formed_env_has_no_dup
[978, 1]
[1000, 34]
cases h1
hd : Definition tl : List Definition ih : Env.WellFormed tl β†’ List.Pairwise (fun d1 d2 => d1.name = d2.name β†’ d1.args.length = d2.args.length β†’ False) tl h1 : (βˆ€ d' ∈ tl, hd.name = d'.name β†’ hd.args.length = d'.args.length β†’ False) ∧ IsMetaVarOrAllDefInEnv tl hd.F ∧ Env.WellFormed tl ⊒ Env.Nodup (hd :: tl)
case intro hd : Definition tl : List Definition ih : Env.WellFormed tl β†’ List.Pairwise (fun d1 d2 => d1.name = d2.name β†’ d1.args.length = d2.args.length β†’ False) tl left✝ : βˆ€ d' ∈ tl, hd.name = d'.name β†’ hd.args.length = d'.args.length β†’ False right✝ : IsMetaVarOrAllDefInEnv tl hd.F ∧ Env.WellFormed tl ⊒ Env.Nodup (hd :: tl)