url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/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
Ο : Instantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
TACTIC:
|
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
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E (phi.imp_ psi)
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (phi.imp_ psi... | E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi β§ IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarOrAllDefInEnv E (sub Ο met... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E (phi.imp_ p... |
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
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi β§ IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarOrAllDefInEnv E (sub Ο met... | E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi β§ IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarOrAllDefInEnv E ((sub Ο me... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi β§ IsMet... |
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
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi β§ IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarOrAllDefInEnv E ((sub Ο me... | E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi β§ IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarOrAllDefInEnv E (sub Ο met... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi β§ IsMet... |
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
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi β§ IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarOrAllDefInEnv E (sub Ο met... | case intro
E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
leftβ : IsMetaVarOrAllDefInEnv E phi
rightβ : IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarOrAll... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1 : IsMetaVarOrAllDefInEnv E phi β§ IsMet... |
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
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1_left : IsMetaVarOrAllDefInEnv E phi
h1_right : IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarOrAllDefInEn... | case left
E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1_left : IsMetaVarOrAllDefInEnv E phi
h1_right : IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarOr... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1_left : IsMetaVarOrAllDefInEnv E phi
h1... |
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
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1_left : IsMetaVarOrAllDefInEnv E phi
h1_right : IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarOr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1_left : IsMetaVarOrAllDefInEn... |
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
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1_left : IsMetaVarOrAllDefInEnv E phi
h1_right : IsMetaVarOrAllDefInEnv E psi
β’ IsMetaVarO... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E : Env
Ο : Instantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
psi_ih : IsMetaVarOrAllDefInEnv E psi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ psi)
h1_left : IsMetaVarOrAllDefInE... |
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
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E (forall_ x phi)
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (forall_ x phi)) | E : Env
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (forall_ x phi)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E (forall_ x phi)
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (forall_ x phi))
TACTIC:
|
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
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (forall_ x phi)) | E : Env
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (forall_ (βΟ x) (sub Ο meta_var_ phi)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (forall_ x phi))
TACTIC:
|
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
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (forall_ (βΟ x) (sub Ο meta_var_ phi)) | E : Env
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (forall_ (βΟ x) (sub Ο meta_var_ phi))
TACTIC:
|
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
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E phi β IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ phi)
TACTIC:
|
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
Ο : Instantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X xs)
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (def_ X xs)) | E : Env
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (def_ X xs)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X xs)
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (def_ X xs))
TACTIC:
|
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
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (def_ X xs)) | E : Env
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (def_ X (List.map (βΟ) xs)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (sub Ο meta_var_ (def_ X xs))
TACTIC:
|
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
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (def_ X (List.map (βΟ) xs)) | E : Env
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β d β E, X = d.name β§ (List.map (βΟ) xs).length = d.args.length | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (def_ X (List.map (βΟ) xs))
TACTIC:
|
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
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β d β E, X = d.name β§ (List.map (βΟ) xs).length = d.args.length | E : Env
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β d β E, X = d.name β§ xs.length = d.args.length | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β d β E, X = d.name β§ (List.map (βΟ) xs).length = d.args.length
TACTIC:
|
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
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β d β E, X = d.name β§ xs.length = d.args.length | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
X : DefName
xs : List VarName
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β d β E, X = d.name β§ xs.length = d.args.length
TACTIC:
|
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
β’ E.Nodup | case nil
h1 : Env.WellFormed []
β’ Env.Nodup []
case cons
headβ : Definition
tailβ : List Definition
tail_ihβ : Env.WellFormed tailβ β Env.Nodup tailβ
h1 : Env.WellFormed (headβ :: tailβ)
β’ Env.Nodup (headβ :: tailβ) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
h1 : E.WellFormed
β’ E.Nodup
TACTIC:
|
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 []
β’ Env.Nodup [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
h1 : Env.WellFormed []
β’ Env.Nodup []
TACTIC:
|
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 []
β’ Env.Nodup [] | h1 : Env.WellFormed []
β’ List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) [] | Please generate a tactic in lean4 to solve the state.
STATE:
h1 : Env.WellFormed []
β’ Env.Nodup []
TACTIC:
|
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 []
β’ List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
h1 : Env.WellFormed []
β’ List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) []
TACTIC:
|
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)
β’ 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)
β’ Env.Nodup (hd :: tl) | Please generate a tactic in lean4 to solve the state.
STATE:
hd : Definition
tl : List Definition
ih : Env.WellFormed tl β Env.Nodup tl
h1 : Env.WellFormed (hd :: tl)
β’ Env.Nodup (hd :: tl)
TACTIC:
|
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)
β’ 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 :
(β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False) β§
IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
β’ Env.Nodup (hd :: tl) | Please generate a tactic in lean4 to solve the state.
STATE:
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)
β’ Env.Nodup (hd :: tl)
TACTIC:
|
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 :
(β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False) β§
IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
β’ 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
leftβ : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
rightβ : IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
β’ Env.Nodup (hd ... | Please generate a tactic in lean4 to solve the state.
STATE:
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 :
(β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False) β§
IsMetaVarOrAllDefIn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.well_formed_env_has_no_dup | [978, 1] | [1000, 34] | cases h1_right | 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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right : IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
β’ 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
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
leftβ : IsMetaVarOrAllDefInEnv tl hd.F
rightβ : Env.WellFormed tl
β’ Env.No... | Please generate a tactic in lean4 to solve the state.
STATE:
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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right : IsMetaVarOrAl... |
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 | 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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ E... | 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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ L... | Please generate a tactic in lean4 to solve the state.
STATE:
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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.well_formed_env_has_no_dup | [978, 1] | [1000, 34] | simp | 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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ L... | 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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ (... | Please generate a tactic in lean4 to solve the state.
STATE:
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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.well_formed_env_has_no_dup | [978, 1] | [1000, 34] | constructor | 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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ (... | case left
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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFor... | Please generate a tactic in lean4 to solve the state.
STATE:
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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.well_formed_env_has_no_dup | [978, 1] | [1000, 34] | exact h1_left | case left
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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFor... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.well_formed_env_has_no_dup | [978, 1] | [1000, 34] | exact ih h1_right_right | case right
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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
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_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | induction E generalizing F | E E' : Env
F : Formula
h1 : β E1, E' = E1 ++ E
h2 : IsMetaVarOrAllDefInEnv E F
β’ IsMetaVarOrAllDefInEnv E' F | case nil
E' : Env
F : Formula
h1 : β E1, E' = E1 ++ []
h2 : IsMetaVarOrAllDefInEnv [] F
β’ IsMetaVarOrAllDefInEnv E' F
case cons
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
F : Formula
h1 : β E1, ... | Please generate a tactic in lean4 to solve the state.
STATE:
E E' : Env
F : Formula
h1 : β E1, E' = E1 ++ E
h2 : IsMetaVarOrAllDefInEnv E F
β’ IsMetaVarOrAllDefInEnv E' F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | case nil.def_ X xs =>
unfold IsMetaVarOrAllDefInEnv at h2
simp at h2 | E' : Env
h1 : β E1, E' = E1 ++ []
X : DefName
xs : List VarName
h2 : IsMetaVarOrAllDefInEnv [] (def_ X xs)
β’ IsMetaVarOrAllDefInEnv E' (def_ X xs) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
h1 : β E1, E' = E1 ++ []
X : DefName
xs : List VarName
h2 : IsMetaVarOrAllDefInEnv [] (def_ X xs)
β’ IsMetaVarOrAllDefInEnv E' (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | induction F | case cons
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
F : Formula
h1 : β E1, E' = E1 ++ headβ :: tailβ
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) F
β’ IsMetaVarOrAllDefInEnv E' F | case cons.meta_var_
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
aβ : MetaVarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (meta_var_ aβ)
β’ IsMetaVarOrAllDe... | Please generate a tactic in lean4 to solve the state.
STATE:
case cons
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
F : Formula
h1 : β E1, E' = E1 ++ headβ :: tailβ
h2 : IsMetaVarOrAllDefInEnv (hea... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | case meta_var_ X =>
unfold IsMetaVarOrAllDefInEnv
simp only | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : MetaVarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (meta_var_ X)
β’ IsMetaVarOrAllDefInEnv E' (meta_var_ X... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : MetaVarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | case pred_ X xs =>
unfold IsMetaVarOrAllDefInEnv
simp only | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : PredName
xs : List VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (pred_ X xs)
β’ IsMetaVarOrAllDefInEnv E... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : PredName
xs : List VarName
h2 : IsMetaVarOrAllDefI... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | case eq_ x y =>
unfold IsMetaVarOrAllDefInEnv
simp only | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x y : VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (eq_ x y)
β’ IsMetaVarOrAllDefInEnv E' (eq_ x y) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x y : VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: ta... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | case true_ =>
unfold IsMetaVarOrAllDefInEnv
simp only | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) true_
β’ IsMetaVarOrAllDefInEnv E' true_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) true_
β’ I... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | case not_ phi phi_ih =>
unfold IsMetaVarOrAllDefInEnv at h2
unfold IsMetaVarOrAllDefInEnv
exact phi_ih h2 | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 : IsMetaVarOr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | case forall_ x phi phi_ih =>
unfold IsMetaVarOrAllDefInEnv at h2
unfold IsMetaVarOrAllDefInEnv
exact phi_ih h2 | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefIn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : MetaVarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (meta_var_ X)
β’ IsMetaVarOrAllDefInEnv E' (meta_var_ X... | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : MetaVarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (meta_var_ X)
β’ True | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : MetaVarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | simp only | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : MetaVarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (meta_var_ X)
β’ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : MetaVarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : PredName
xs : List VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (pred_ X xs)
β’ IsMetaVarOrAllDefInEnv E... | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : PredName
xs : List VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (pred_ X xs)
β’ True | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : PredName
xs : List VarName
h2 : IsMetaVarOrAllDefI... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | simp only | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : PredName
xs : List VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (pred_ X xs)
β’ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
X : PredName
xs : List VarName
h2 : IsMetaVarOrAllDefI... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x y : VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (eq_ x y)
β’ IsMetaVarOrAllDefInEnv E' (eq_ x y) | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x y : VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (eq_ x y)
β’ True | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x y : VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: ta... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | simp only | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x y : VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) (eq_ x y)
β’ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x y : VarName
h2 : IsMetaVarOrAllDefInEnv (headβ :: ta... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) true_
β’ IsMetaVarOrAllDefInEnv E' true_ | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) true_
β’ True | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) true_
β’ I... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | simp only | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) true_
β’ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
h2 : IsMetaVarOrAllDefInEnv (headβ :: tailβ) true_
β’ T... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv at h2 | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 : IsMetaVarOr... | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 : IsMetaVarOr... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 : IsMetaVarOr... | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 : IsMetaVarOr... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | exact phi_ih h2 | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 : IsMetaVarOr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv at h2 | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
psi_ih : IsM... | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
psi_ih : IsM... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (hea... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
psi_ih : IsM... | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
psi_ih : IsM... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (hea... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | cases h2 | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
psi_ih : IsM... | case intro
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
p... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (hea... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | constructor | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
psi_ih : IsM... | case left
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
ps... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (hea... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | exact phi_ih h2_left | case left
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
ps... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDef... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | exact psi_ih h2_right | case right
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
p... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
phi psi : Formula
phi_ih : IsMetaVarOrAllDe... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv at h2 | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 :... | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 :... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefIn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 :... | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 :... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefIn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | exact phi_ih h2 | E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv (headβ :: tailβ) phi β IsMetaVarOrAllDefInEnv E' phi
h2 :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
headβ : Definition
tailβ : List Definition
tail_ihβ : β (F : Formula), (β E1, E' = E1 ++ tailβ) β IsMetaVarOrAllDefInEnv tailβ F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ headβ :: tailβ
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefIn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv at h2 | E' : Env
h1 : β E1, E' = E1 ++ []
X : DefName
xs : List VarName
h2 : IsMetaVarOrAllDefInEnv [] (def_ X xs)
β’ IsMetaVarOrAllDefInEnv E' (def_ X xs) | E' : Env
h1 : β E1, E' = E1 ++ []
X : DefName
xs : List VarName
h2 : β d β [], X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E' (def_ X xs) | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
h1 : β E1, E' = E1 ++ []
X : DefName
xs : List VarName
h2 : IsMetaVarOrAllDefInEnv [] (def_ X xs)
β’ IsMetaVarOrAllDefInEnv E' (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | simp at h2 | E' : Env
h1 : β E1, E' = E1 ++ []
X : DefName
xs : List VarName
h2 : β d β [], X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E' (def_ X xs) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
h1 : β E1, E' = E1 ++ []
X : DefName
xs : List VarName
h2 : β d β [], X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E' (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv at h2 | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
β’ IsMetaVarOrAllDefInEnv E' (def_ X xs) | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E' (de... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : IsMetaVarOrAllDefInEnv (E_hd ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | apply Exists.elim h1 | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E' (de... | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
β’ β (a : Env), E' = a ++ E_hd :... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | intro E1 h1_1 | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
β’ β (a : Env), E' = a ++ E_hd :... | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | apply Exists.elim h2 | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | intro d h2_1 | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | cases h2_1 | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | case intro
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' =... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | simp at h2_1_left | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | cases h2_1_left | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | case inl
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | apply Exists.intro E_hd | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | simp only [h1_1] | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | constructor | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | case left
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = ... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | simp | case left
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl,... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | simp only [β c1] | case right
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' =... | case right
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' =... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | exact h2_1_right | case right
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | apply E_ih | E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1 ++ E_hd... | case h1
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | Please generate a tactic in lean4 to solve the state.
STATE:
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | apply Exists.intro (E1 ++ [E_hd]) | case h1
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | case h1
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | simp | case h1
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | case h1
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | exact h1_1 | case h1
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | unfold IsMetaVarOrAllDefInEnv | case h2
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | case h2
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | apply Exists.intro d | case h2
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | case h2
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | constructor | case h2
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E' = E1... | case h2.left
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E'... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | exact c1 | case h2.left
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E'... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2.left
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.concat_env_preserves_is_meta_var_or_all_def_in_env | [1003, 1] | [1079, 29] | exact h2_1_right | case h2.right
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E_tl, X = d.name β§ xs.length = d.args.length
E1 : Env
h1_1 : E... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2.right
E' : Env
E_hd : Definition
E_tl : List Definition
E_ih : β (F : Formula), (β E1, E' = E1 ++ E_tl) β IsMetaVarOrAllDefInEnv E_tl F β IsMetaVarOrAllDefInEnv E' F
h1 : β E1, E' = E1 ++ E_hd :: E_tl
X : DefName
xs : List VarName
h2 : β d β E_hd :: E... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | induction E | E : Env
d : Definition
h1 : E.WellFormed
h2 : d β E
β’ IsMetaVarOrAllDefInEnv E d.F | case nil
d : Definition
h1 : Env.WellFormed []
h2 : d β []
β’ IsMetaVarOrAllDefInEnv [] d.F
case cons
d headβ : Definition
tailβ : List Definition
tail_ihβ : Env.WellFormed tailβ β d β tailβ β IsMetaVarOrAllDefInEnv tailβ d.F
h1 : Env.WellFormed (headβ :: tailβ)
h2 : d β headβ :: tailβ
β’ IsMetaVarOrAllDefInEnv (headβ :... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
d : Definition
h1 : E.WellFormed
h2 : d β E
β’ IsMetaVarOrAllDefInEnv E d.F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | case nil =>
simp at h2 | d : Definition
h1 : Env.WellFormed []
h2 : d β []
β’ IsMetaVarOrAllDefInEnv [] d.F | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
d : Definition
h1 : Env.WellFormed []
h2 : d β []
β’ IsMetaVarOrAllDefInEnv [] d.F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | simp at h2 | d : Definition
h1 : Env.WellFormed []
h2 : d β []
β’ IsMetaVarOrAllDefInEnv [] d.F | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
d : Definition
h1 : Env.WellFormed []
h2 : d β []
β’ IsMetaVarOrAllDefInEnv [] d.F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | unfold Env.WellFormed at h1 | d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1 : Env.WellFormed (hd :: tl)
h2 : d β hd :: tl
β’ IsMetaVarOrAllDefInEnv (hd :: tl) d.F | d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d β hd :: tl
h1 :
(β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False) β§
IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
β’ IsMetaVarOrAllDefInEnv (hd :: tl) d.F | Please generate a tactic in lean4 to solve the state.
STATE:
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1 : Env.WellFormed (hd :: tl)
h2 : d β hd :: tl
β’ IsMetaVarOrAllDefInEnv (hd :: tl) d.F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | simp at h2 | d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d β hd :: tl
h1 :
(β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False) β§
IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
β’ IsMetaVarOrAllDefInEnv (hd :: tl) d.F | d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1 :
(β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False) β§
IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
h2 : d = hd β¨ d β tl
β’ IsMetaVarOrAllDefInEnv (hd :: tl) d.F | Please generate a tactic in lean4 to solve the state.
STATE:
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d β hd :: tl
h1 :
(β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False) β§
IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
β’... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | cases h1 | d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1 :
(β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False) β§
IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
h2 : d = hd β¨ d β tl
β’ IsMetaVarOrAllDefInEnv (hd :: tl) d.F | case intro
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
leftβ : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
rightβ : IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
β’ IsMetaVarOrAllDefInEnv (hd :: tl) d.F | Please generate a tactic in lean4 to solve the state.
STATE:
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1 :
(β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False) β§
IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
h2 : d = hd β¨ d β t... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | cases h1_right | d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right : IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFormed tl
β’ IsMetaVarOrAllDefInEnv (hd :: tl) d.F | case intro
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
leftβ : IsMetaVarOrAllDefInEnv tl hd.F
rightβ : Env.WellFormed tl
β’ IsMetaVarOrAllDefInEnv (hd :: tl) d.... | Please generate a tactic in lean4 to solve the state.
STATE:
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right : IsMetaVarOrAllDefInEnv tl hd.F β§ Env.WellFo... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | apply concat_env_preserves_is_meta_var_or_all_def_in_env tl (hd :: tl) | d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ IsMetaVarOrAllDefInEnv (hd :: t... | case h1
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ β E1, hd :: tl = E1 ++ ... | Please generate a tactic in lean4 to solve the state.
STATE:
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_righ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | apply Exists.intro [hd] | case h1
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ β E1, hd :: tl = E1 ++ ... | case h1
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ hd :: tl = [hd] ++ tl | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | simp | case h1
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ hd :: tl = [hd] ++ tl | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | cases h2 | case h2
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
β’ IsMetaVarOrAllDefInEnv ... | case h2.inl
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
hβ : d = hd
β’ IsMetaVarOrAllDefInEnv tl d.... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h2 : d = hd β¨ d β tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | case _ c1 =>
subst c1
exact h1_right_left | d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
c1 : d = hd
β’ IsMetaVarOrAllDefInEnv tl d.F | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFor... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | case _ c1 =>
exact ih h1_right_right c1 | d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
c1 : d β tl
β’ IsMetaVarOrAllDefInEnv tl d.F | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFor... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | subst c1 | d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFormed tl
c1 : d = hd
β’ IsMetaVarOrAllDefInEnv tl d.F | d : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1_right_right : Env.WellFormed tl
h1_left : β d' β tl, d.name = d'.name β d.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl d.F
β’ IsMetaVarOrAllDefInEnv tl d.F | Please generate a tactic in lean4 to solve the state.
STATE:
d hd : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl hd.F
h1_right_right : Env.WellFor... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_in_well_formed_env_is_meta_var_or_all_def_in_env | [1082, 1] | [1109, 39] | exact h1_right_left | d : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1_right_right : Env.WellFormed tl
h1_left : β d' β tl, d.name = d'.name β d.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl d.F
β’ IsMetaVarOrAllDefInEnv tl d.F | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
d : Definition
tl : List Definition
ih : Env.WellFormed tl β d β tl β IsMetaVarOrAllDefInEnv tl d.F
h1_right_right : Env.WellFormed tl
h1_left : β d' β tl, d.name = d'.name β d.args.length = d'.args.length β False
h1_right_left : IsMetaVarOrAllDefInEnv tl d.F... |
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