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 |
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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 | σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1 : (phi.imp_ psi).metaVarSet = ∅
⊢ sub σ τ (phi.imp_ psi) = sub σ τ' (phi.imp_ psi) | σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1 : phi.metaVarSet ∪ psi.metaVarSet = ∅
⊢ sub σ τ (phi.imp_ psi) = sub σ τ' (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 | σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1 : phi.metaVarSet ∪ psi.metaVarSet = ∅
⊢ sub σ τ (phi.imp_ psi) = sub σ τ' (phi.imp_ psi) | σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1 : phi.metaVarSet = ∅ ∧ psi.metaVarSet = ∅
⊢ sub σ τ (phi.imp_ psi) = sub σ τ' (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 | σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1 : phi.metaVarSet = ∅ ∧ psi.metaVarSet = ∅
⊢ sub σ τ (phi.imp_ psi) = sub σ τ' (phi.imp_ psi) | σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1 : phi.metaVarSet = ∅ ∧ psi.metaVarSet = ∅
⊢ (sub σ τ phi).imp_ (sub σ τ psi) = (sub σ τ' phi).imp_ (sub σ τ' 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 | σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1 : phi.metaVarSet = ∅ ∧ psi.metaVarSet = ∅
⊢ (sub σ τ phi).imp_ (sub σ τ psi) = (sub σ τ' phi).imp_ (sub σ τ' psi) | case intro
σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
left✝ : phi.metaVarSet = ∅
right✝ : psi.metaVarSet = ∅
⊢ (sub σ τ phi).imp_ (sub σ τ psi) = (sub σ τ' phi).imp_ (sub σ τ' 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 | σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1_left : phi.metaVarSet = ∅
h1_right : psi.metaVarSet = ∅
⊢ (sub σ τ phi).imp_ (sub σ τ psi) = (sub σ τ' phi).imp_ (sub σ τ' psi) | case h.e'_1
σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1_left : phi.metaVarSet = ∅
h1_right : psi.metaVarSet = ∅
⊢ sub σ τ phi = sub σ τ' phi
case h.e'_2
σ : Instantiation
τ τ' : MetaIns... |
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
σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1_left : phi.metaVarSet = ∅
h1_right : psi.metaVarSet = ∅
⊢ sub σ τ phi = sub σ τ' 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
σ : Instantiation
τ τ' : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
psi_ih : psi.metaVarSet = ∅ → sub σ τ psi = sub σ τ' psi
h1_left : phi.metaVarSet = ∅
h1_right : psi.metaVarSet = ∅
⊢ sub σ τ psi = sub σ τ' 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 | σ : Instantiation
τ τ' : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
h1 : (forall_ x phi).metaVarSet = ∅
⊢ sub σ τ (forall_ x phi) = sub σ τ' (forall_ x phi) | σ : Instantiation
τ τ' : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
h1 : phi.metaVarSet = ∅
⊢ sub σ τ (forall_ x phi) = sub σ τ' (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 | σ : Instantiation
τ τ' : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
h1 : phi.metaVarSet = ∅
⊢ sub σ τ (forall_ x phi) = sub σ τ' (forall_ x phi) | σ : Instantiation
τ τ' : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
h1 : phi.metaVarSet = ∅
⊢ forall_ (↑σ x) (sub σ τ phi) = forall_ (↑σ x) (sub σ τ' 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 | σ : Instantiation
τ τ' : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
h1 : phi.metaVarSet = ∅
⊢ forall_ (↑σ x) (sub σ τ phi) = forall_ (↑σ x) (sub σ τ' phi) | case h.e'_2
σ : Instantiation
τ τ' : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
h1 : phi.metaVarSet = ∅
⊢ sub σ τ phi = sub σ τ' 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
σ : Instantiation
τ τ' : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
h1 : phi.metaVarSet = ∅
⊢ sub σ τ phi = sub σ τ' 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 | σ : Instantiation
τ τ' : MetaInstantiation
X : DefName
xs : List VarName
h1 : (def_ X xs).metaVarSet = ∅
⊢ sub σ τ (def_ X xs) = sub σ τ' (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
σ : Instantiation
τ : MetaInstantiation
h1 : NoMetaVarAndAllFreeInList vs F
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ F) | case meta_var_
σ : Instantiation
τ : MetaInstantiation
a✝ : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ a✝)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (meta_var_ a✝))
case pred_
σ : Instantiation
τ : MetaInstantiation
a✝¹ : PredName
a✝ vs : List VarName
h1 : NoMetaVarAndAllF... |
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 | σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ X)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (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 σ.1 h1 | σ : Instantiation
τ : MetaInstantiation
X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (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 | σ : Instantiation
τ : MetaInstantiation
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs true_
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ 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 | σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi.not_
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ 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 | σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (forall_ x phi)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (f... | 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 σ.val h1 | σ : Instantiation
τ : MetaInstantiation
X : DefName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (def_ X xs)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (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 | σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ X)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (meta_var_ X)) | σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
vs : List VarName
h1 : False
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (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 | σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
vs : List VarName
h1 : False
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (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 | σ : Instantiation
τ : MetaInstantiation
X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (pred_ X xs)) | σ : Instantiation
τ : 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 | σ : Instantiation
τ : MetaInstantiation
X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (pred_ X (List.map (↑σ) xs)) | σ : Instantiation
τ : MetaInstantiation
X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
⊢ List.map (↑σ) xs ⊆ 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 σ.1 h1 | σ : Instantiation
τ : MetaInstantiation
X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
⊢ List.map (↑σ) xs ⊆ 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 | σ : Instantiation
τ : MetaInstantiation
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs true_
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ true_) | σ : Instantiation
τ : 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 | σ : Instantiation
τ : MetaInstantiation
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs true_
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) true_ | σ : Instantiation
τ : 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 | σ : Instantiation
τ : 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 | σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi.not_
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi.not_) | σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ 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 | σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi.not_) | σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ 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 | σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi).not_ | σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ 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 | σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ 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 | σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ psi)
vs : L... | σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ psi)
vs : L... |
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 | σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ psi)
vs : L... | σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ psi)
vs : L... |
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 | σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ psi)
vs : L... | σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ psi)
vs : L... |
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 | σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ psi)
vs : L... | case intro
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ ... |
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 | σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ psi)
vs : L... | case left
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ p... |
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
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ p... | 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
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
psi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ ... | 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 | σ : Instantiation
τ : MetaInstantiation
x y : VarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (eq_ x y)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (eq_ x y)) | σ : Instantiation
τ : MetaInstantiation
x y : VarName
vs : List VarName
h1 : x ∈ vs ∧ y ∈ vs
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (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 | σ : Instantiation
τ : MetaInstantiation
x y : VarName
vs : List VarName
h1 : x ∈ vs ∧ y ∈ vs
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (eq_ x y)) | σ : Instantiation
τ : 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 | σ : Instantiation
τ : MetaInstantiation
x y : VarName
vs : List VarName
h1 : x ∈ vs ∧ y ∈ vs
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (eq_ (↑σ x) (↑σ y)) | σ : Instantiation
τ : 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 | σ : Instantiation
τ : 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
σ : Instantiation
τ : 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 | σ : Instantiation
τ : 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
σ : Instantiation
τ : MetaInstantiation
x y : VarName
vs : List VarName
h1_left : x ∈ vs
h1_right : y ∈ vs
⊢ ↑σ x ∈ List.map (↑σ) vs
case right
σ : Instantiation
τ : 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 σ.val h1_left | case left
σ : Instantiation
τ : 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 σ.val h1_right | case right
σ : Instantiation
τ : 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 | σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (forall_ x phi)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (f... | σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (forall... |
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 | σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (forall... | σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (forall_ (↑σ 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] | unfold NoMetaVarAndAllFreeInList | σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (forall_ (↑σ x) ... | σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
⊢ NoMetaVarAndAllFreeInList (↑σ x :: List.map (↑σ) vs) (sub σ τ... |
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] | σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
⊢ NoMetaVarAndAllFreeInList (↑σ x :: List.map (↑σ) vs) (sub σ τ... | σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) (x :: vs)) (sub σ τ ... |
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 | σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) (x :: vs)) (sub σ τ ... | 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 | σ : Instantiation
τ : MetaInstantiation
X : DefName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (def_ X xs)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (def_ X xs)) | σ : Instantiation
τ : 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 | σ : Instantiation
τ : MetaInstantiation
X : DefName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (def_ X xs)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (def_ X (List.map (↑σ) xs)) | σ : Instantiation
τ : MetaInstantiation
X : DefName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (def_ X xs)
⊢ List.map (↑σ) xs ⊆ 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 σ.val h1 | σ : Instantiation
τ : MetaInstantiation
X : DefName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (def_ X xs)
⊢ List.map (↑σ) xs ⊆ 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
σ : Instantiation
h1 : IsMetaVarOrAllDefInEnv E F
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ F) | case meta_var_
E : Env
σ : Instantiation
a✝ : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ a✝)
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ (meta_var_ a✝))
case pred_
E : Env
σ : Instantiation
a✝¹ : PredName
a✝ : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ a✝¹ a✝)
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_va... |
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
σ : Instantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
h1 : IsMetaVarOrAllDefInEnv E true_
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi.not_
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E (forall_ x phi)
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X xs)
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ (meta_var_ X)) | E : Env
σ : 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
σ : Instantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
⊢ IsMetaVarOrAllDefInEnv E (meta_var_ X) | E : Env
σ : 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
σ : 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
σ : Instantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ (pred_ X xs)) | E : Env
σ : 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
σ : Instantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
⊢ IsMetaVarOrAllDefInEnv E (pred_ X (List.map (↑σ) xs)) | E : Env
σ : 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
σ : 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
σ : Instantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ (eq_ x y)) | E : Env
σ : 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
σ : Instantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
⊢ IsMetaVarOrAllDefInEnv E (eq_ (↑σ x) (↑σ y)) | E : Env
σ : 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
σ : 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
σ : Instantiation
h1 : IsMetaVarOrAllDefInEnv E true_
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ true_) | E : Env
σ : 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
σ : Instantiation
h1 : IsMetaVarOrAllDefInEnv E true_
⊢ IsMetaVarOrAllDefInEnv E true_ | E : Env
σ : 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
σ : 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
σ : Instantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi.not_
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi.not_) | E : Env
σ : Instantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi.not_) | E : Env
σ : Instantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi).not_ | E : Env
σ : Instantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E (phi.imp_ psi)
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ (phi.imp_ psi... | E : Env
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarOrAllDefInEnv E (sub σ met... |
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
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarOrAllDefInEnv E (sub σ met... | E : Env
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarOrAllDefInEnv E ((sub σ me... |
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
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarOrAllDefInEnv E ((sub σ me... | E : Env
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarOrAllDefInEnv E (sub σ met... |
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
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi ∧ IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarOrAllDefInEnv E (sub σ met... | case intro
E : Env
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
left✝ : IsMetaVarOrAllDefInEnv E phi
right✝ : IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarOrAll... |
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
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1_left : IsMetaVarOrAllDefInEnv E phi
h1_right : IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarOrAllDefInEn... | case left
E : Env
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1_left : IsMetaVarOrAllDefInEnv E phi
h1_right : IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarOr... |
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
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1_left : IsMetaVarOrAllDefInEnv E phi
h1_right : IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarOr... | 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
σ : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ psi)
h1_left : IsMetaVarOrAllDefInEnv E phi
h1_right : IsMetaVarOrAllDefInEnv E psi
⊢ IsMetaVarO... | 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
σ : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E (forall_ x phi)
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ (forall_ x phi)) | E : Env
σ : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ (forall_ x phi)) | E : Env
σ : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (forall_ (↑σ x) (sub σ 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
σ : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (forall_ (↑σ x) (sub σ meta_var_ phi)) | E : Env
σ : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi → IsMetaVarOrAllDefInEnv E (sub σ meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X xs)
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ (def_ X xs)) | E : Env
σ : Instantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ IsMetaVarOrAllDefInEnv E (sub σ 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
σ : Instantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ IsMetaVarOrAllDefInEnv E (sub σ meta_var_ (def_ X xs)) | E : Env
σ : Instantiation
X : DefName
xs : List VarName
h1 : ∃ 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
σ : Instantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ IsMetaVarOrAllDefInEnv E (def_ X (List.map (↑σ) xs)) | E : Env
σ : Instantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ ∃ 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
σ : Instantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ ∃ d ∈ E, X = d.name ∧ (List.map (↑σ) xs).length = d.args.length | E : Env
σ : Instantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ ∃ 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
σ : Instantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ ∃ 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✝ → 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 → d1.args.length = d2.args.length → 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 → d1.args.length = d2.args.length → 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 → Env.Nodup tl
h1 : Env.WellFormed (hd :: tl)
⊢ Env.Nodup (hd :: tl) | hd : Definition
tl : List Definition
ih : Env.WellFormed tl → List.Pairwise (fun d1 d2 => d1.name = d2.name → d1.args.length = d2.args.length → 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 → List.Pairwise (fun d1 d2 => d1.name = d2.name → d1.args.length = d2.args.length → False) tl
h1 : Env.WellFormed (hd :: tl)
⊢ Env.Nodup (hd :: tl) | hd : Definition
tl : List Definition
ih : Env.WellFormed tl → List.Pairwise (fun d1 d2 => d1.name = d2.name → d1.args.length = d2.args.length → False) tl
h1 :
(∀ d' ∈ tl, hd.name = d'.name → hd.args.length = d'.args.length → 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 → List.Pairwise (fun d1 d2 => d1.name = d2.name → d1.args.length = d2.args.length → False) tl
h1 :
(∀ d' ∈ tl, hd.name = d'.name → hd.args.length = d'.args.length → False) ∧
IsMetaVarOrAllDefInEnv tl hd.F ∧ Env.WellFormed tl
⊢ Env.Nodup (hd :: tl) | case intro
hd : Definition
tl : List Definition
ih : Env.WellFormed tl → List.Pairwise (fun d1 d2 => d1.name = d2.name → d1.args.length = d2.args.length → False) tl
left✝ : ∀ d' ∈ tl, hd.name = d'.name → hd.args.length = d'.args.length → False
right✝ : IsMetaVarOrAllDefInEnv tl hd.F ∧ Env.WellFormed tl
⊢ Env.Nodup (hd ... |
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