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.lem_2_a | [1766, 1] | [1837, 13] | exact h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h2 : ∀ X_1 ∈ (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (τ X_1)
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h2 : ∀ X_1 ∈ (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (τ X_1)
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | induction F | E : Env
σ : Instantiation
τ : MetaInstantiation
F : Formula
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ F)
⊢ IsMetaVarOrAllDefInEnv E F | case meta_var_
E : Env
σ : Instantiation
τ : MetaInstantiation
a✝ : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (meta_var_ a✝))
⊢ IsMetaVarOrAllDefInEnv E (meta_var_ a✝)
case pred_
E : Env
σ : Instantiation
τ : MetaInstantiation
a✝¹ : PredName
a✝ : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (pred_ a✝¹ ... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
F : Formula
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ F)
⊢ IsMetaVarOrAllDefInEnv E F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | case meta_var_ X =>
unfold IsMetaVarOrAllDefInEnv
simp only | E : Env
σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (meta_var_ X))
⊢ IsMetaVarOrAllDefInEnv E (meta_var_ X) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (meta_var_ X))
⊢ IsMetaVarOrAllDefInEnv E (meta_var_ X)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | case pred_ X xs =>
unfold IsMetaVarOrAllDefInEnv
simp only | E : Env
σ : Instantiation
τ : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (pred_ X xs))
⊢ IsMetaVarOrAllDefInEnv E (pred_ X xs) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (pred_ X xs))
⊢ IsMetaVarOrAllDefInEnv E (pred_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | case eq_ x y =>
unfold IsMetaVarOrAllDefInEnv
simp only | E : Env
σ : Instantiation
τ : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (eq_ x y))
⊢ IsMetaVarOrAllDefInEnv E (eq_ x y) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (eq_ x y))
⊢ IsMetaVarOrAllDefInEnv E (eq_ x y)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | case true_ =>
unfold IsMetaVarOrAllDefInEnv
simp only | E : Env
σ : Instantiation
τ : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ true_)
⊢ IsMetaVarOrAllDefInEnv E true_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ true_)
⊢ IsMetaVarOrAllDefInEnv E true_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | case not_ phi phi_ih =>
unfold sub at h1
unfold IsMetaVarOrAllDefInEnv at h1
unfold IsMetaVarOrAllDefInEnv
exact phi_ih h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi.not_)
⊢ IsMetaVarOrAllDefInEnv E phi.not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi.not_)
⊢ IsMetaVarOrAllDefInEnv E phi.not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | case forall_ x phi phi_ih =>
unfold sub at h1
unfold IsMetaVarOrAllDefInEnv at h1
unfold IsMetaVarOrAllDefInEnv
exact phi_ih h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (forall_ x phi))
⊢ IsMetaVarOrAllDefInEnv E (forall_ x phi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (forall_ x phi))
⊢ IsMetaVarOrAllDefInEnv E (forall_ x phi)
TACTIC:... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | case def_ X xs =>
unfold sub at h1
unfold IsMetaVarOrAllDefInEnv at h1
simp at h1
unfold IsMetaVarOrAllDefInEnv
exact h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (def_ X xs))
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (def_ X xs))
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (meta_var_ X))
⊢ IsMetaVarOrAllDefInEnv E (meta_var_ X) | E : Env
σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (meta_var_ X))
⊢ True | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (meta_var_ X))
⊢ IsMetaVarOrAllDefInEnv E (meta_var_ X)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | simp only | E : Env
σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (meta_var_ X))
⊢ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (meta_var_ X))
⊢ True
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
σ : Instantiation
τ : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (pred_ X xs))
⊢ IsMetaVarOrAllDefInEnv E (pred_ X xs) | E : Env
σ : Instantiation
τ : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (pred_ X xs))
⊢ True | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (pred_ X xs))
⊢ IsMetaVarOrAllDefInEnv E (pred_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | simp only | E : Env
σ : Instantiation
τ : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (pred_ X xs))
⊢ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (pred_ X xs))
⊢ True
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
σ : Instantiation
τ : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (eq_ x y))
⊢ IsMetaVarOrAllDefInEnv E (eq_ x y) | E : Env
σ : Instantiation
τ : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (eq_ x y))
⊢ True | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (eq_ x y))
⊢ IsMetaVarOrAllDefInEnv E (eq_ x y)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | simp only | E : Env
σ : Instantiation
τ : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (eq_ x y))
⊢ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (eq_ x y))
⊢ True
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
σ : Instantiation
τ : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ true_)
⊢ IsMetaVarOrAllDefInEnv E true_ | E : Env
σ : Instantiation
τ : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ true_)
⊢ True | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ true_)
⊢ IsMetaVarOrAllDefInEnv E true_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | simp only | E : Env
σ : Instantiation
τ : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ true_)
⊢ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ true_)
⊢ True
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold sub at h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi.not_)
⊢ IsMetaVarOrAllDefInEnv E phi.not_ | E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi).not_
⊢ IsMetaVarOrAllDefInEnv E phi.not_ | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi.not_)
⊢ IsMetaVarOrAllDefInEnv E phi.not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv at h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi).not_
⊢ IsMetaVarOrAllDefInEnv E phi.not_ | E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E phi.not_ | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi).not_
⊢ IsMetaVarOrAllDefInEnv E phi.not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E phi.not_ | E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E phi | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E phi.not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | exact phi_ih h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold sub at h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (phi.imp_ psi))
⊢ IsMetaVarOrAllDefInEnv E (phi.imp_ psi) | E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E ((sub σ τ phi).imp_ (sub σ τ psi))
⊢ IsMetaVarOrAllDefInEnv E (phi... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E (sub ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv at h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E ((sub σ τ phi).imp_ (sub σ τ psi))
⊢ IsMetaVarOrAllDefInEnv E (phi... | E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi) ∧ IsMetaVarOrAllDefInEnv E (sub σ τ psi)
⊢ IsMetaVar... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E ((sub... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi) ∧ IsMetaVarOrAllDefInEnv E (sub σ τ psi)
⊢ IsMetaVar... | E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi) ∧ IsMetaVarOrAllDefInEnv E (sub σ τ psi)
⊢ IsMetaVar... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E (sub ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | cases h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi) ∧ IsMetaVarOrAllDefInEnv E (sub σ τ psi)
⊢ IsMetaVar... | case intro
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
left✝ : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
right✝ : IsMetaVarOrAllDefInEnv E (sub... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1 : IsMetaVarOrAllDefInEnv E (sub ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | constructor | E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1_left : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
h1_right : IsMetaVarOrAllDefInEnv E (sub σ τ ps... | case left
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1_left : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
h1_right : IsMetaVarOrAllDefInEnv E (... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1_left : IsMetaVarOrAllDefInEnv E ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | exact phi_ih h1_left | case left
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1_left : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
h1_right : IsMetaVarOrAllDefInEnv E (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1_left : IsMetaVarOrAllD... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | exact psi_ih h1_right | case right
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1_left : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
h1_right : IsMetaVarOrAllDefInEnv E ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E : Env
σ : Instantiation
τ : MetaInstantiation
phi psi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
psi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ psi) → IsMetaVarOrAllDefInEnv E psi
h1_left : IsMetaVarOrAll... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold sub at h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (forall_ x phi))
⊢ IsMetaVarOrAllDefInEnv E (forall_ x phi) | E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (forall_ (↑σ x) (sub σ τ phi))
⊢ IsMetaVarOrAllDefInEnv E (forall_ x phi) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (forall_ x phi))
⊢ IsMetaVarOrAllDefInEnv E (forall_ x phi)
TACTIC:... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv at h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (forall_ (↑σ x) (sub σ τ phi))
⊢ IsMetaVarOrAllDefInEnv E (forall_ x phi) | E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E (forall_ x phi) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (forall_ (↑σ x) (sub σ τ phi))
⊢ IsMetaVarOrAllDefInEnv E (forall_ x phi)
TA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E (forall_ x phi) | E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E phi | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E (forall_ x phi)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | exact phi_ih h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih : IsMetaVarOrAllDefInEnv E (sub σ τ phi) → IsMetaVarOrAllDefInEnv E phi
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ phi)
⊢ IsMetaVarOrAllDefInEnv E phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold sub at h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (def_ X xs))
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs) | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X (List.map (↑σ) xs))
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (sub σ τ (def_ X xs))
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv at h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X (List.map (↑σ) xs))
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs) | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ (List.map (↑σ) xs).length = d.args.length
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X (List.map (↑σ) xs))
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | simp at h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ (List.map (↑σ) xs).length = d.args.length
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs) | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ (List.map (↑σ) xs).length = d.args.length
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs) | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ IsMetaVarOrAllDefInEnv E (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_b | [1840, 1] | [1889, 13] | exact h1 | E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
σ : Instantiation
τ : MetaInstantiation
X : DefName
xs : List VarName
h1 : ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
⊢ ∃ d ∈ E, X = d.name ∧ xs.length = d.args.length
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | induction h1 | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1 : IsProof E Γ Δ F
⊢ IsMetaVarOrAllDefInEnv E F | case hyp
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
Γ✝ : List (VarName × MetaVarName)
Δ✝ : List Formula
phi✝ : Formula
a✝¹ : IsMetaVarOrAllDefInEnv E phi✝
a✝ : phi✝ ∈ Δ✝
⊢ IsMetaVarOrAllDefInEnv E phi✝
case mp
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
Γ✝ : List (V... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1 : IsProof E Γ Δ F
⊢ IsMetaVarOrAllDefInEnv E F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case hyp h1_Γ h1_Δ h1_phi h1_1 h1_2 =>
exact h1_1 | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi ∈ h1_Δ
⊢ IsMetaVarOrAllDefInEnv E h1_phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi ∈ h1_Δ
⊢ IsMetaVarOrAllDefInEnv E h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case mp h1_Γ h1_Δ h1_phi h1_psi h1_1 h1_2 h1_ih_1 h1_ih_2 =>
unfold IsMetaVarOrAllDefInEnv at h1_ih_2
cases h1_ih_2
case intro h1_ih_2_left h1_ih_2_right =>
exact h1_ih_2_right | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_ih_2 : IsMetaVarOrAllDefInEnv E (h1_phi.imp... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 : IsMetaVarOrAllDef... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case prop_1 h1_Γ h1_Δ h1_phi h1_psi h1_1 h1_2 =>
repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E (h1_phi.imp_ (h1_psi.imp_ h1_phi)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E (h1_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case prop_2 h1_Γ h1_Δ h1_phi h1_psi h1_chi h1_1 h1_2 h1_3 =>
repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_chi
⊢ IsMetaVarOrAllDefInEnv E ((h1_phi.imp_ (h1_p... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDef... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case prop_3 h1_Γ h1_Δ h1_phi h1_psi h1_1 h1_2 =>
repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E ((h1_phi.not_.imp_ h1_psi.not_).imp_ (h1_psi.imp_ h1_phi)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E ((h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case gen h1_Γ h1_Δ h1_phi h1_x h1_1 h1_ih =>
repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_ih : IsMetaVarOrAllDefInEnv E h1_phi
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x h1_phi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_ih : IsMetaVarOrAllDefInEnv E h1_phi
⊢ IsMetaVarOrAllDefInEnv E ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case pred_1 h1_Γ h1_Δ h1_phi h1_psi h1_x h1_1 h1_2 =>
repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E ((forall_ h1_x (h1_phi.imp_ h1_psi)).imp_ ((forall... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAll... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case pred_2 h1_Γ h1_Δ h1_phi h1_x h1_1 h1_2 =>
repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDefInEnv E (h1_phi.imp_ (forall_ h1_x h1_phi)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDefInEnv E (h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case eq_1 h1_Γ h1_Δ h1_x h1_y h1_1 =>
unfold exists_
repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (exists_ h1_x (eq_ h1_x h1_y)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (exists_ h1_x (eq_ h1_x h1_y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case eq_2 h1_Γ h1_Δ h1_x h1_y h1_z =>
unfold IsMetaVarOrAllDefInEnv
repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E ((eq_ h1_x h1_y).imp_ ((eq_ h1_x h1_z).imp_ (eq_ h1_y h1_z))) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E ((eq_ h1_x h1_y).imp_ ((eq_ h1_x h1_z).imp_ (eq_ h1_y h1_z)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case eq_3 h1_Γ h1_Δ h1_n h1_name h1_xs h1_ys =>
sorry | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_n : ℕ
h1_name : PredName
h1_xs h1_ys : Fin h1_n → VarName
⊢ IsMetaVarOrAllDefInEnv E (eqSubPred h1_name h1_n h1_xs h1_ys) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_n : ℕ
h1_name : PredName
h1_xs h1_ys : Fin h1_n → VarName
⊢ IsMetaVarOrAllDefInEnv E (eqSubPred h1_name h1_n h1_xs h1_ys)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case thm h1_Γ h1_Γ' h1_Δ h1_Δ' h1_phi h1_σ h1_τ h1_1 h1_2 h1_3 h1_4 h1_ih_1 h1_ih_2 =>
exact lem_2_a E h1_σ h1_τ h1_phi h1_ih_2 h1_1 | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ h1_Γ' : List (VarName × MetaVarName)
h1_Δ h1_Δ' : List Formula
h1_phi : Formula
h1_σ : Instantiation
h1_τ : MetaInstantiation
h1_1 : ∀ X ∈ h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_τ X)
h1_2 : ∀ (x : VarName) (X : MetaVarName), (x, X) ∈ h1... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ h1_Γ' : List (VarName × MetaVarName)
h1_Δ h1_Δ' : List Formula
h1_phi : Formula
h1_σ : Instantiation
h1_τ : MetaInstantiation
h1_1 : ∀ X ∈ h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case conv h1_Γ h1_Δ h1_phi h1_phi' h1_1 h1_2 h1_3 h1_ih =>
exact h1_1 | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Γ h1_Δ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_ih : IsMetaVarOrAllDefInEnv E h1_phi
⊢ IsMetaVarOrAllDefInEnv... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Γ h1_Δ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | exact h1_1 | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi ∈ h1_Δ
⊢ IsMetaVarOrAllDefInEnv E h1_phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi ∈ h1_Δ
⊢ IsMetaVarOrAllDefInEnv E h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | unfold IsMetaVarOrAllDefInEnv at h1_ih_2 | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_ih_2 : IsMetaVarOrAllDefInEnv E (h1_phi.imp... | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_ih_2 : IsMetaVarOrAllDefInEnv E h1_phi ∧ Is... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 : IsMetaVarOrAllDef... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | cases h1_ih_2 | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_ih_2 : IsMetaVarOrAllDefInEnv E h1_phi ∧ Is... | case intro
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 left✝ : IsMetaVarOrAllDefInEnv E h1_phi
right✝ : IsMetaVarOrAllDefInE... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 : IsMetaVarOrAllDef... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | case intro h1_ih_2_left h1_ih_2_right =>
exact h1_ih_2_right | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 h1_ih_2_left : IsMetaVarOrAllDefInEnv E h1_phi
h1_ih_2_right : IsMetaVarOrAllDef... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 h1_ih_2_left : IsMe... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | exact h1_ih_2_right | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 h1_ih_2_left : IsMetaVarOrAllDefInEnv E h1_phi
h1_ih_2_right : IsMetaVarOrAllDef... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_2 : IsProof E h1_Γ h1_Δ (h1_phi.imp_ h1_psi)
h1_ih_1 h1_ih_2_left : IsMe... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E (h1_phi.imp_ (h1_psi.imp_ h1_phi)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E (h1_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | first | constructor | assumption | case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E h1_phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | constructor | case right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E (h1_psi.imp_ h1_phi) | case right.left
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E h1_psi
case right.right
E : Env
Γ : List (VarNam... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefI... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | assumption | case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E h1_phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_chi
⊢ IsMetaVarOrAllDefInEnv E ((h1_phi.imp_ (h1_p... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDef... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | first | constructor | assumption | case right.right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_chi
⊢ IsMetaVarOrAllDefInEn... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | constructor | case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_chi
⊢ IsMetaVarOrAllDefInEnv E (h... | case right.right.left
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_chi
⊢ IsMetaVarOrAllDefInEnv... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | assumption | case right.right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_chi
⊢ IsMetaVarOrAllDefInEn... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E ((h1_phi.not_.imp_ h1_psi.not_).imp_ (h1_psi.imp_ h1_phi)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E ((h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_ih : IsMetaVarOrAllDefInEnv E h1_phi
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x h1_phi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_ih : IsMetaVarOrAllDefInEnv E h1_phi
⊢ IsMetaVarOrAllDefInEnv E ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_ih : IsMetaVarOrAllDefInEnv E h1_phi
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x h1_phi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_ih : IsMetaVarOrAllDefInEnv E h1_phi
⊢ IsMetaVarOrAllDefInEnv E ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_ih : IsMetaVarOrAllDefInEnv E h1_phi
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x h1_phi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Γ h1_Δ h1_phi
h1_ih : IsMetaVarOrAllDefInEnv E h1_phi
⊢ IsMetaVarOrAllDefInEnv E ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E ((forall_ h1_x (h1_phi.imp_ h1_psi)).imp_ ((forall... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAll... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | first | constructor | assumption | case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x h1_psi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | constructor | case right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E ((forall_ h1_x h1_phi).imp_ (forall_ h1... | case right.left
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x h1_phi)
case right.... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsM... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | assumption | case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x h1_psi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDefInEnv E (h1_phi.imp_ (forall_ h1_x h1_phi)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDefInEnv E (h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | first | constructor | assumption | case right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x h1_phi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDef... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | constructor | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDefInEnv E (h1_phi.imp_ (forall_ h1_x h1_phi)) | case left
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDefInEnv E h1_phi
case right
E : Env
Γ : List (VarName × MetaVar... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDefInEnv E (h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | assumption | case right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x h1_phi) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Γ h1_x h1_phi
⊢ IsMetaVarOrAllDef... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | unfold exists_ | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (exists_ h1_x (eq_ h1_x h1_y)) | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x (eq_ h1_x h1_y).not_).not_ | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (exists_ h1_x (eq_ h1_x h1_y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x (eq_ h1_x h1_y).not_).not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x (eq_ h1_x h1_y).not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x (eq_ h1_x h1_y).not_).not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x (eq_ h1_x h1_y).not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | constructor | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x (eq_ h1_x h1_y).not_).not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y : VarName
h1_1 : ¬h1_y = h1_x
⊢ IsMetaVarOrAllDefInEnv E (forall_ h1_x (eq_ h1_x h1_y).not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | unfold IsMetaVarOrAllDefInEnv | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E ((eq_ h1_x h1_y).imp_ ((eq_ h1_x h1_z).imp_ (eq_ h1_y h1_z))) | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E (eq_ h1_x h1_y) ∧ IsMetaVarOrAllDefInEnv E ((eq_ h1_x h1_z).imp_ (eq_ h1_y h1_z)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E ((eq_ h1_x h1_y).imp_ ((eq_ h1_x h1_z).imp_ (eq_ h1_y h1_z)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | repeat first | constructor | assumption | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E (eq_ h1_x h1_y) ∧ IsMetaVarOrAllDefInEnv E ((eq_ h1_x h1_z).imp_ (eq_ h1_y h1_z)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E (eq_ h1_x h1_y) ∧ IsMetaVarOrAllDefInEnv E ((eq_ h1_x h1_z).imp_ (eq_ h1_y h1_z))... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | first | constructor | assumption | case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E (eq_ h1_y h1_z) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E (eq_ h1_y h1_z)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | constructor | case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E (eq_ h1_y h1_z) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_x h1_y h1_z : VarName
⊢ IsMetaVarOrAllDefInEnv E (eq_ h1_y h1_z)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | sorry | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_n : ℕ
h1_name : PredName
h1_xs h1_ys : Fin h1_n → VarName
⊢ IsMetaVarOrAllDefInEnv E (eqSubPred h1_name h1_n h1_xs h1_ys) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_n : ℕ
h1_name : PredName
h1_xs h1_ys : Fin h1_n → VarName
⊢ IsMetaVarOrAllDefInEnv E (eqSubPred h1_name h1_n h1_xs h1_ys)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | exact lem_2_a E h1_σ h1_τ h1_phi h1_ih_2 h1_1 | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ h1_Γ' : List (VarName × MetaVarName)
h1_Δ h1_Δ' : List Formula
h1_phi : Formula
h1_σ : Instantiation
h1_τ : MetaInstantiation
h1_1 : ∀ X ∈ h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_τ X)
h1_2 : ∀ (x : VarName) (X : MetaVarName), (x, X) ∈ h1... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ h1_Γ' : List (VarName × MetaVarName)
h1_Δ h1_Δ' : List Formula
h1_phi : Formula
h1_σ : Instantiation
h1_τ : MetaInstantiation
h1_1 : ∀ X ∈ h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.is_proof_imp_is_meta_var_or_all_def_in_env | [1892, 1] | [1932, 15] | exact h1_1 | E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Γ h1_Δ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_ih : IsMetaVarOrAllDefInEnv E h1_phi
⊢ IsMetaVarOrAllDefInEnv... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Γ : List (VarName × MetaVarName)
Δ : List Formula
F : Formula
h1_Γ : List (VarName × MetaVarName)
h1_Δ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Γ h1_Δ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | induction E | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
E : Env
d : Definition
name : DefName
args : List VarName
h1 : E.WellFormed
h2 : d ∈ E
h3 : name = d.name ∧ args.length = d.args.length
⊢ Holds D I (Function.updateListITE V d.args (List.map V args)) M E d.F ↔ Holds D I V M E (def_ name args) | case nil
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
h1 : Env.WellFormed []
h2 : d ∈ []
⊢ Holds D I (Function.updateListITE V d.args (List.map V args)) M [] d.F ↔ Holds D I V M [] (def_ name args)
c... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
E : Env
d : Definition
name : DefName
args : List VarName
h1 : E.WellFormed
h2 : d ∈ E
h3 : name = d.name ∧ args.length = d.args.length
⊢ Holds D I (Function.updateListITE V d.args (List.map V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | case nil =>
simp at h2 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
h1 : Env.WellFormed []
h2 : d ∈ []
⊢ Holds D I (Function.updateListITE V d.args (List.map V args)) M [] d.F ↔ Holds D I V M [] (def_ name args) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
h1 : Env.WellFormed []
h2 : d ∈ []
⊢ Holds D I (Function.updateListITE V d.args (List.map V ar... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | simp at h2 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
h1 : Env.WellFormed []
h2 : d ∈ []
⊢ Holds D I (Function.updateListITE V d.args (List.map V args)) M [] d.F ↔ Holds D I V M [] (def_ name args) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
h1 : Env.WellFormed []
h2 : d ∈ []
⊢ Holds D I (Function.updateListITE V d.args (List.map V ar... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | have s1 : Env.Nodup (hd :: tl) := well_formed_env_has_no_dup (hd :: tl) h1 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | have s2 : ∃ E1 : Env, (hd :: tl) = E1 ++ tl | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | case s2
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | apply Exists.intro [hd] | case s2
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M... | case s2
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M... | Please generate a tactic in lean4 to solve the state.
STATE:
case s2
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | simp | case s2
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | Please generate a tactic in lean4 to solve the state.
STATE:
case s2
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | unfold Env.WellFormed at h1 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | simp at h2 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | cases h1 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | case intro
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | cases h1_right | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | case intro
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | simp only [Holds] | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | split_ifs | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | case pos
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I (Function.updateListITE V d.args (List.map V args)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name ∧ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl →
d ∈ tl →
(Holds D I ... |
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