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https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | apply Exists.elim Ο.2 | Ο : Instantiation
β’ β Ο_inv, βΟ β βΟ_inv = id β§ βΟ_inv β βΟ = id | Ο : Instantiation
β’ β (a : VarName β VarName), βΟ β a = id β§ a β βΟ = id β β Ο_inv, βΟ β βΟ_inv = id β§ βΟ_inv β βΟ = id |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | intro Ο' a1 | Ο : Instantiation
β’ β (a : VarName β VarName), βΟ β a = id β§ a β βΟ = id β β Ο_inv, βΟ β βΟ_inv = id β§ βΟ_inv β βΟ = id | Ο : Instantiation
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ β Ο_inv, βΟ β βΟ_inv = id β§ βΟ_inv β βΟ = id |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | cases a1 | Ο : Instantiation
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ β Ο_inv, βΟ β βΟ_inv = id β§ βΟ_inv β βΟ = id | case intro
Ο : Instantiation
Ο' : VarName β VarName
leftβ : βΟ β Ο' = id
rightβ : Ο' β βΟ = id
β’ β Ο_inv, βΟ β βΟ_inv = id β§ βΟ_inv β βΟ = id |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | apply Exists.intro Ο_inv | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
Ο_inv : Instantiation := β¨Ο', β―β©
β’ β Ο_inv, βΟ β βΟ_inv = id β§ βΟ_inv β βΟ = id | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
Ο_inv : Instantiation := β¨Ο', β―β©
β’ βΟ β βΟ_inv = id β§ βΟ_inv β βΟ = id |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | constructor | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
Ο_inv : Instantiation := β¨Ο', β―β©
β’ βΟ β βΟ_inv = id β§ βΟ_inv β βΟ = id | case left
Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
Ο_inv : Instantiation := β¨Ο', β―β©
β’ βΟ β βΟ_inv = id
case right
Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
Ο_inv : Instantiation := β¨Ο', β―β©
β’ βΟ_inv β βΟ = id |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | apply Exists.intro Ο.1 | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ β Ο'_1, Ο' β Ο'_1 = id β§ Ο'_1 β Ο' = id | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ Ο' β βΟ = id β§ βΟ β Ο' = id |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | constructor | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ Ο' β βΟ = id β§ βΟ β Ο' = id | case left
Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ Ο' β βΟ = id
case right
Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ βΟ β Ο' = id |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | exact a1_right | case left
Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ Ο' β βΟ = id | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | exact a1_left | case right
Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ βΟ β Ο' = id | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | exact a1_left | case left
Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
Ο_inv : Instantiation := β¨Ο', β―β©
β’ βΟ β βΟ_inv = id | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.has_left_right_inverse | [684, 1] | [705, 21] | exact a1_right | case right
Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
Ο_inv : Instantiation := β¨Ο', β―β©
β’ βΟ_inv β βΟ = id | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_injective | [708, 1] | [716, 44] | obtain β¨Ο', a1β© := Ο.2 | Ο : Instantiation
β’ Function.Injective βΟ | case intro
Ο : Instantiation
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Function.Injective βΟ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_injective | [708, 1] | [716, 44] | cases a1 | case intro
Ο : Instantiation
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Function.Injective βΟ | case intro.intro
Ο : Instantiation
Ο' : VarName β VarName
leftβ : βΟ β Ο' = id
rightβ : Ο' β βΟ = id
β’ Function.Injective βΟ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_injective | [708, 1] | [716, 44] | case intro a1_left a1_right =>
have s1 : Function.LeftInverse Ο' Ο.1 := congr_fun a1_right
exact Function.LeftInverse.injective s1 | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ Function.Injective βΟ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_injective | [708, 1] | [716, 44] | have s1 : Function.LeftInverse Ο' Ο.1 := congr_fun a1_right | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ Function.Injective βΟ | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
s1 : Function.LeftInverse Ο' βΟ
β’ Function.Injective βΟ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_injective | [708, 1] | [716, 44] | exact Function.LeftInverse.injective s1 | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
s1 : Function.LeftInverse Ο' βΟ
β’ Function.Injective βΟ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_surjective | [719, 1] | [727, 46] | obtain β¨Ο', a1β© := Ο.2 | Ο : Instantiation
β’ Function.Surjective βΟ | case intro
Ο : Instantiation
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Function.Surjective βΟ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_surjective | [719, 1] | [727, 46] | cases a1 | case intro
Ο : Instantiation
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Function.Surjective βΟ | case intro.intro
Ο : Instantiation
Ο' : VarName β VarName
leftβ : βΟ β Ο' = id
rightβ : Ο' β βΟ = id
β’ Function.Surjective βΟ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_surjective | [719, 1] | [727, 46] | case intro a1_left a1_right =>
have s1 : Function.RightInverse Ο' Ο.1 := congr_fun a1_left
exact Function.RightInverse.surjective s1 | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ Function.Surjective βΟ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_surjective | [719, 1] | [727, 46] | have s1 : Function.RightInverse Ο' Ο.1 := congr_fun a1_left | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
β’ Function.Surjective βΟ | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
s1 : Function.RightInverse Ο' βΟ
β’ Function.Surjective βΟ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_surjective | [719, 1] | [727, 46] | exact Function.RightInverse.surjective s1 | Ο : Instantiation
Ο' : VarName β VarName
a1_left : βΟ β Ο' = id
a1_right : Ο' β βΟ = id
s1 : Function.RightInverse Ο' βΟ
β’ Function.Surjective βΟ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_bijective | [730, 1] | [737, 40] | unfold Function.Bijective | Ο : Instantiation
β’ Function.Bijective βΟ | Ο : Instantiation
β’ Function.Injective βΟ β§ Function.Surjective βΟ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_bijective | [730, 1] | [737, 40] | constructor | Ο : Instantiation
β’ Function.Injective βΟ β§ Function.Surjective βΟ | case left
Ο : Instantiation
β’ Function.Injective βΟ
case right
Ο : Instantiation
β’ Function.Surjective βΟ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_bijective | [730, 1] | [737, 40] | exact Instantiation.is_injective Ο | case left
Ο : Instantiation
β’ Function.Injective βΟ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.Instantiation.is_bijective | [730, 1] | [737, 40] | exact Instantiation.is_surjective Ο | case right
Ο : Instantiation
β’ Function.Surjective βΟ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | induction F | F : Formula
Ο Ο' : Instantiation
β’ sub Ο meta_var_ (sub Ο' meta_var_ F) = sub (Ο.comp Ο') meta_var_ F | case meta_var_
Ο Ο' : Instantiation
aβ : MetaVarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (meta_var_ aβ)) = sub (Ο.comp Ο') meta_var_ (meta_var_ aβ)
case pred_
Ο Ο' : Instantiation
aβΒΉ : PredName
aβ : List VarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (pred_ aβΒΉ aβ)) = sub (Ο.comp Ο') meta_var_ (pred_ aβΒΉ aβ)
case eq_
Ο Ο' : Instantiation
aβΒΉ aβ : VarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (eq_ aβΒΉ aβ)) = sub (Ο.comp Ο') meta_var_ (eq_ aβΒΉ aβ)
case true_
Ο Ο' : Instantiation
β’ sub Ο meta_var_ (sub Ο' meta_var_ true_) = sub (Ο.comp Ο') meta_var_ true_
case not_
Ο Ο' : Instantiation
aβ : Formula
a_ihβ : sub Ο meta_var_ (sub Ο' meta_var_ aβ) = sub (Ο.comp Ο') meta_var_ aβ
β’ sub Ο meta_var_ (sub Ο' meta_var_ aβ.not_) = sub (Ο.comp Ο') meta_var_ aβ.not_
case imp_
Ο Ο' : Instantiation
aβΒΉ aβ : Formula
a_ihβΒΉ : sub Ο meta_var_ (sub Ο' meta_var_ aβΒΉ) = sub (Ο.comp Ο') meta_var_ aβΒΉ
a_ihβ : sub Ο meta_var_ (sub Ο' meta_var_ aβ) = sub (Ο.comp Ο') meta_var_ aβ
β’ sub Ο meta_var_ (sub Ο' meta_var_ (aβΒΉ.imp_ aβ)) = sub (Ο.comp Ο') meta_var_ (aβΒΉ.imp_ aβ)
case forall_
Ο Ο' : Instantiation
aβΒΉ : VarName
aβ : Formula
a_ihβ : sub Ο meta_var_ (sub Ο' meta_var_ aβ) = sub (Ο.comp Ο') meta_var_ aβ
β’ sub Ο meta_var_ (sub Ο' meta_var_ (forall_ aβΒΉ aβ)) = sub (Ο.comp Ο') meta_var_ (forall_ aβΒΉ aβ)
case def_
Ο Ο' : Instantiation
aβΒΉ : DefName
aβ : List VarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (def_ aβΒΉ aβ)) = sub (Ο.comp Ο') meta_var_ (def_ aβΒΉ aβ) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | case meta_var_ X =>
rfl | Ο Ο' : Instantiation
X : MetaVarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (meta_var_ X)) = sub (Ο.comp Ο') meta_var_ (meta_var_ X) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | case pred_ X xs =>
simp only [sub]
unfold Instantiation.comp
simp | Ο Ο' : Instantiation
X : PredName
xs : List VarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (pred_ X xs)) = sub (Ο.comp Ο') meta_var_ (pred_ X xs) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | case eq_ x y =>
rfl | Ο Ο' : Instantiation
x y : VarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (eq_ x y)) = sub (Ο.comp Ο') meta_var_ (eq_ x y) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | case true_ =>
rfl | Ο Ο' : Instantiation
β’ sub Ο meta_var_ (sub Ο' meta_var_ true_) = sub (Ο.comp Ο') meta_var_ true_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | case not_ phi phi_ih =>
simp only [sub]
unfold Instantiation.comp
congr! 1 | Ο Ο' : Instantiation
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ sub Ο meta_var_ (sub Ο' meta_var_ phi.not_) = sub (Ο.comp Ο') meta_var_ phi.not_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | case imp_ phi psi phi_ih psi_ih =>
simp only [sub]
unfold Instantiation.comp
congr! 1 | Ο Ο' : Instantiation
phi psi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
psi_ih : sub Ο meta_var_ (sub Ο' meta_var_ psi) = sub (Ο.comp Ο') meta_var_ psi
β’ sub Ο meta_var_ (sub Ο' meta_var_ (phi.imp_ psi)) = sub (Ο.comp Ο') meta_var_ (phi.imp_ psi) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | case forall_ x phi phi_ih =>
simp only [sub]
unfold Instantiation.comp
congr! 1 | Ο Ο' : Instantiation
x : VarName
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ sub Ο meta_var_ (sub Ο' meta_var_ (forall_ x phi)) = sub (Ο.comp Ο') meta_var_ (forall_ x phi) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | case def_ X xs =>
simp only [sub]
unfold Instantiation.comp
simp | Ο Ο' : Instantiation
X : DefName
xs : List VarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (def_ X xs)) = sub (Ο.comp Ο') meta_var_ (def_ X xs) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | rfl | Ο Ο' : Instantiation
X : MetaVarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (meta_var_ X)) = sub (Ο.comp Ο') meta_var_ (meta_var_ X) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | simp only [sub] | Ο Ο' : Instantiation
X : PredName
xs : List VarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (pred_ X xs)) = sub (Ο.comp Ο') meta_var_ (pred_ X xs) | Ο Ο' : Instantiation
X : PredName
xs : List VarName
β’ pred_ X (List.map (βΟ) (List.map (βΟ') xs)) = pred_ X (List.map (β(Ο.comp Ο')) xs) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | unfold Instantiation.comp | Ο Ο' : Instantiation
X : PredName
xs : List VarName
β’ pred_ X (List.map (βΟ) (List.map (βΟ') xs)) = pred_ X (List.map (β(Ο.comp Ο')) xs) | Ο Ο' : Instantiation
X : PredName
xs : List VarName
β’ pred_ X (List.map (βΟ) (List.map (βΟ') xs)) = pred_ X (List.map (ββ¨βΟ β βΟ', β―β©) xs) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | simp | Ο Ο' : Instantiation
X : PredName
xs : List VarName
β’ pred_ X (List.map (βΟ) (List.map (βΟ') xs)) = pred_ X (List.map (ββ¨βΟ β βΟ', β―β©) xs) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | rfl | Ο Ο' : Instantiation
x y : VarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (eq_ x y)) = sub (Ο.comp Ο') meta_var_ (eq_ x y) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | rfl | Ο Ο' : Instantiation
β’ sub Ο meta_var_ (sub Ο' meta_var_ true_) = sub (Ο.comp Ο') meta_var_ true_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | simp only [sub] | Ο Ο' : Instantiation
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ sub Ο meta_var_ (sub Ο' meta_var_ phi.not_) = sub (Ο.comp Ο') meta_var_ phi.not_ | Ο Ο' : Instantiation
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ (sub Ο meta_var_ (sub Ο' meta_var_ phi)).not_ = (sub (Ο.comp Ο') meta_var_ phi).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | unfold Instantiation.comp | Ο Ο' : Instantiation
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ (sub Ο meta_var_ (sub Ο' meta_var_ phi)).not_ = (sub (Ο.comp Ο') meta_var_ phi).not_ | Ο Ο' : Instantiation
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ (sub Ο meta_var_ (sub Ο' meta_var_ phi)).not_ = (sub β¨βΟ β βΟ', β―β© meta_var_ phi).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | congr! 1 | Ο Ο' : Instantiation
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ (sub Ο meta_var_ (sub Ο' meta_var_ phi)).not_ = (sub β¨βΟ β βΟ', β―β© meta_var_ phi).not_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | simp only [sub] | Ο Ο' : Instantiation
phi psi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
psi_ih : sub Ο meta_var_ (sub Ο' meta_var_ psi) = sub (Ο.comp Ο') meta_var_ psi
β’ sub Ο meta_var_ (sub Ο' meta_var_ (phi.imp_ psi)) = sub (Ο.comp Ο') meta_var_ (phi.imp_ psi) | Ο Ο' : Instantiation
phi psi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
psi_ih : sub Ο meta_var_ (sub Ο' meta_var_ psi) = sub (Ο.comp Ο') meta_var_ psi
β’ (sub Ο meta_var_ (sub Ο' meta_var_ phi)).imp_ (sub Ο meta_var_ (sub Ο' meta_var_ psi)) =
(sub (Ο.comp Ο') meta_var_ phi).imp_ (sub (Ο.comp Ο') meta_var_ psi) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | unfold Instantiation.comp | Ο Ο' : Instantiation
phi psi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
psi_ih : sub Ο meta_var_ (sub Ο' meta_var_ psi) = sub (Ο.comp Ο') meta_var_ psi
β’ (sub Ο meta_var_ (sub Ο' meta_var_ phi)).imp_ (sub Ο meta_var_ (sub Ο' meta_var_ psi)) =
(sub (Ο.comp Ο') meta_var_ phi).imp_ (sub (Ο.comp Ο') meta_var_ psi) | Ο Ο' : Instantiation
phi psi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
psi_ih : sub Ο meta_var_ (sub Ο' meta_var_ psi) = sub (Ο.comp Ο') meta_var_ psi
β’ (sub Ο meta_var_ (sub Ο' meta_var_ phi)).imp_ (sub Ο meta_var_ (sub Ο' meta_var_ psi)) =
(sub β¨βΟ β βΟ', β―β© meta_var_ phi).imp_ (sub β¨βΟ β βΟ', β―β© meta_var_ psi) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | congr! 1 | Ο Ο' : Instantiation
phi psi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
psi_ih : sub Ο meta_var_ (sub Ο' meta_var_ psi) = sub (Ο.comp Ο') meta_var_ psi
β’ (sub Ο meta_var_ (sub Ο' meta_var_ phi)).imp_ (sub Ο meta_var_ (sub Ο' meta_var_ psi)) =
(sub β¨βΟ β βΟ', β―β© meta_var_ phi).imp_ (sub β¨βΟ β βΟ', β―β© meta_var_ psi) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | simp only [sub] | Ο Ο' : Instantiation
x : VarName
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ sub Ο meta_var_ (sub Ο' meta_var_ (forall_ x phi)) = sub (Ο.comp Ο') meta_var_ (forall_ x phi) | Ο Ο' : Instantiation
x : VarName
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ forall_ (βΟ (βΟ' x)) (sub Ο meta_var_ (sub Ο' meta_var_ phi)) =
forall_ (β(Ο.comp Ο') x) (sub (Ο.comp Ο') meta_var_ phi) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | unfold Instantiation.comp | Ο Ο' : Instantiation
x : VarName
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ forall_ (βΟ (βΟ' x)) (sub Ο meta_var_ (sub Ο' meta_var_ phi)) =
forall_ (β(Ο.comp Ο') x) (sub (Ο.comp Ο') meta_var_ phi) | Ο Ο' : Instantiation
x : VarName
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ forall_ (βΟ (βΟ' x)) (sub Ο meta_var_ (sub Ο' meta_var_ phi)) =
forall_ (ββ¨βΟ β βΟ', β―β© x) (sub β¨βΟ β βΟ', β―β© meta_var_ phi) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | congr! 1 | Ο Ο' : Instantiation
x : VarName
phi : Formula
phi_ih : sub Ο meta_var_ (sub Ο' meta_var_ phi) = sub (Ο.comp Ο') meta_var_ phi
β’ forall_ (βΟ (βΟ' x)) (sub Ο meta_var_ (sub Ο' meta_var_ phi)) =
forall_ (ββ¨βΟ β βΟ', β―β© x) (sub β¨βΟ β βΟ', β―β© meta_var_ phi) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | simp only [sub] | Ο Ο' : Instantiation
X : DefName
xs : List VarName
β’ sub Ο meta_var_ (sub Ο' meta_var_ (def_ X xs)) = sub (Ο.comp Ο') meta_var_ (def_ X xs) | Ο Ο' : Instantiation
X : DefName
xs : List VarName
β’ def_ X (List.map (βΟ) (List.map (βΟ') xs)) = def_ X (List.map (β(Ο.comp Ο')) xs) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | unfold Instantiation.comp | Ο Ο' : Instantiation
X : DefName
xs : List VarName
β’ def_ X (List.map (βΟ) (List.map (βΟ') xs)) = def_ X (List.map (β(Ο.comp Ο')) xs) | Ο Ο' : Instantiation
X : DefName
xs : List VarName
β’ def_ X (List.map (βΟ) (List.map (βΟ') xs)) = def_ X (List.map (ββ¨βΟ β βΟ', β―β©) xs) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_of_sub_is_sub_of_instantiation_comp | [740, 1] | [772, 9] | simp | Ο Ο' : Instantiation
X : DefName
xs : List VarName
β’ def_ X (List.map (βΟ) (List.map (βΟ') xs)) = def_ X (List.map (ββ¨βΟ β βΟ', β―β©) xs) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | induction F | F : Formula
Ο : Instantiation
Ο : MetaInstantiation
h1 : F.metaVarSet = β
β’ (sub Ο Ο F).metaVarSet = β
| case meta_var_
Ο : Instantiation
Ο : MetaInstantiation
aβ : MetaVarName
h1 : (meta_var_ aβ).metaVarSet = β
β’ (sub Ο Ο (meta_var_ aβ)).metaVarSet = β
case pred_
Ο : Instantiation
Ο : MetaInstantiation
aβΒΉ : PredName
aβ : List VarName
h1 : (pred_ aβΒΉ aβ).metaVarSet = β
β’ (sub Ο Ο (pred_ aβΒΉ aβ)).metaVarSet = β
case eq_
Ο : Instantiation
Ο : MetaInstantiation
aβΒΉ aβ : VarName
h1 : (eq_ aβΒΉ aβ).metaVarSet = β
β’ (sub Ο Ο (eq_ aβΒΉ aβ)).metaVarSet = β
case true_
Ο : Instantiation
Ο : MetaInstantiation
h1 : true_.metaVarSet = β
β’ (sub Ο Ο true_).metaVarSet = β
case not_
Ο : Instantiation
Ο : MetaInstantiation
aβ : Formula
a_ihβ : aβ.metaVarSet = β
β (sub Ο Ο aβ).metaVarSet = β
h1 : aβ.not_.metaVarSet = β
β’ (sub Ο Ο aβ.not_).metaVarSet = β
case imp_
Ο : Instantiation
Ο : MetaInstantiation
aβΒΉ aβ : Formula
a_ihβΒΉ : aβΒΉ.metaVarSet = β
β (sub Ο Ο aβΒΉ).metaVarSet = β
a_ihβ : aβ.metaVarSet = β
β (sub Ο Ο aβ).metaVarSet = β
h1 : (aβΒΉ.imp_ aβ).metaVarSet = β
β’ (sub Ο Ο (aβΒΉ.imp_ aβ)).metaVarSet = β
case forall_
Ο : Instantiation
Ο : MetaInstantiation
aβΒΉ : VarName
aβ : Formula
a_ihβ : aβ.metaVarSet = β
β (sub Ο Ο aβ).metaVarSet = β
h1 : (forall_ aβΒΉ aβ).metaVarSet = β
β’ (sub Ο Ο (forall_ aβΒΉ aβ)).metaVarSet = β
case def_
Ο : Instantiation
Ο : MetaInstantiation
aβΒΉ : DefName
aβ : List VarName
h1 : (def_ aβΒΉ aβ).metaVarSet = β
β’ (sub Ο Ο (def_ aβΒΉ aβ)).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | case meta_var_ X =>
unfold Formula.metaVarSet at h1
simp at h1 | Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : (meta_var_ X).metaVarSet = β
β’ (sub Ο Ο (meta_var_ X)).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | case pred_ X xs =>
rfl | Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : (pred_ X xs).metaVarSet = β
β’ (sub Ο Ο (pred_ X xs)).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | case eq_ x y =>
rfl | Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : (eq_ x y).metaVarSet = β
β’ (sub Ο Ο (eq_ x y)).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | case true_ =>
rfl | Ο : Instantiation
Ο : MetaInstantiation
h1 : true_.metaVarSet = β
β’ (sub Ο Ο true_).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | case not_ phi phi_ih =>
unfold Formula.metaVarSet at h1
unfold sub
unfold Formula.metaVarSet
exact phi_ih h1 | Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.not_.metaVarSet = β
β’ (sub Ο Ο phi.not_).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | case forall_ x phi phi_ih =>
unfold Formula.metaVarSet at h1
unfold sub
unfold Formula.metaVarSet
exact phi_ih h1 | Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : (forall_ x phi).metaVarSet = β
β’ (sub Ο Ο (forall_ x phi)).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | case def_ X xs =>
rfl | Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h1 : (def_ X xs).metaVarSet = β
β’ (sub Ο Ο (def_ X xs)).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | unfold Formula.metaVarSet at h1 | Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : (meta_var_ X).metaVarSet = β
β’ (sub Ο Ο (meta_var_ X)).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : {X} = β
β’ (sub Ο Ο (meta_var_ X)).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | simp at h1 | Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : {X} = β
β’ (sub Ο Ο (meta_var_ X)).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | rfl | Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : (pred_ X xs).metaVarSet = β
β’ (sub Ο Ο (pred_ X xs)).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | rfl | Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : (eq_ x y).metaVarSet = β
β’ (sub Ο Ο (eq_ x y)).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | rfl | Ο : Instantiation
Ο : MetaInstantiation
h1 : true_.metaVarSet = β
β’ (sub Ο Ο true_).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | unfold Formula.metaVarSet at h1 | Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.not_.metaVarSet = β
β’ (sub Ο Ο phi.not_).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (sub Ο Ο phi.not_).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | unfold sub | Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (sub Ο Ο phi.not_).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (sub Ο Ο phi).not_.metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | unfold Formula.metaVarSet | Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (sub Ο Ο phi).not_.metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | exact phi_ih h1 | Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | unfold Formula.metaVarSet at h1 | Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1 : (phi.imp_ psi).metaVarSet = β
β’ (sub Ο Ο (phi.imp_ psi)).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1 : phi.metaVarSet βͺ psi.metaVarSet = β
β’ (sub Ο Ο (phi.imp_ psi)).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | simp only [Finset.union_eq_empty] at h1 | Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1 : phi.metaVarSet βͺ psi.metaVarSet = β
β’ (sub Ο Ο (phi.imp_ psi)).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1 : phi.metaVarSet = β
β§ psi.metaVarSet = β
β’ (sub Ο Ο (phi.imp_ psi)).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | unfold sub | Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1 : phi.metaVarSet = β
β§ psi.metaVarSet = β
β’ (sub Ο Ο (phi.imp_ psi)).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1 : phi.metaVarSet = β
β§ psi.metaVarSet = β
β’ ((sub Ο Ο phi).imp_ (sub Ο Ο psi)).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | unfold Formula.metaVarSet | Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1 : phi.metaVarSet = β
β§ psi.metaVarSet = β
β’ ((sub Ο Ο phi).imp_ (sub Ο Ο psi)).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1 : phi.metaVarSet = β
β§ psi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet βͺ (sub Ο Ο psi).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | cases h1 | Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1 : phi.metaVarSet = β
β§ psi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet βͺ (sub Ο Ο psi).metaVarSet = β
| case intro
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
leftβ : phi.metaVarSet = β
rightβ : psi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet βͺ (sub Ο Ο psi).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | simp only [Finset.union_eq_empty] | Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1_left : phi.metaVarSet = β
h1_right : psi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet βͺ (sub Ο Ο psi).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1_left : phi.metaVarSet = β
h1_right : psi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet = β
β§ (sub Ο Ο psi).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | constructor | Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1_left : phi.metaVarSet = β
h1_right : psi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet = β
β§ (sub Ο Ο psi).metaVarSet = β
| case left
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1_left : phi.metaVarSet = β
h1_right : psi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet = β
case right
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1_left : phi.metaVarSet = β
h1_right : psi.metaVarSet = β
β’ (sub Ο Ο psi).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | exact phi_ih h1_left | case left
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1_left : phi.metaVarSet = β
h1_right : psi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | exact psi_ih h1_right | case right
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
psi_ih : psi.metaVarSet = β
β (sub Ο Ο psi).metaVarSet = β
h1_left : phi.metaVarSet = β
h1_right : psi.metaVarSet = β
β’ (sub Ο Ο psi).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | unfold Formula.metaVarSet at h1 | Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : (forall_ x phi).metaVarSet = β
β’ (sub Ο Ο (forall_ x phi)).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (sub Ο Ο (forall_ x phi)).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | unfold sub | Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (sub Ο Ο (forall_ x phi)).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (forall_ (βΟ x) (sub Ο Ο phi)).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | unfold Formula.metaVarSet | Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (forall_ (βΟ x) (sub Ο Ο phi)).metaVarSet = β
| Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet = β
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | exact phi_ih h1 | Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = β
β (sub Ο Ο phi).metaVarSet = β
h1 : phi.metaVarSet = β
β’ (sub Ο Ο phi).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.sub_preserves_empty_meta_var_set | [775, 1] | [817, 8] | rfl | Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h1 : (def_ X xs).metaVarSet = β
β’ (sub Ο Ο (def_ X xs)).metaVarSet = β
| no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | induction F | F : Formula
Ο : Instantiation
Ο Ο' : MetaInstantiation
h1 : F.metaVarSet = β
β’ sub Ο Ο F = sub Ο Ο' F | case meta_var_
Ο : Instantiation
Ο Ο' : MetaInstantiation
aβ : MetaVarName
h1 : (meta_var_ aβ).metaVarSet = β
β’ sub Ο Ο (meta_var_ aβ) = sub Ο Ο' (meta_var_ aβ)
case pred_
Ο : Instantiation
Ο Ο' : MetaInstantiation
aβΒΉ : PredName
aβ : List VarName
h1 : (pred_ aβΒΉ aβ).metaVarSet = β
β’ sub Ο Ο (pred_ aβΒΉ aβ) = sub Ο Ο' (pred_ aβΒΉ aβ)
case eq_
Ο : Instantiation
Ο Ο' : MetaInstantiation
aβΒΉ aβ : VarName
h1 : (eq_ aβΒΉ aβ).metaVarSet = β
β’ sub Ο Ο (eq_ aβΒΉ aβ) = sub Ο Ο' (eq_ aβΒΉ aβ)
case true_
Ο : Instantiation
Ο Ο' : MetaInstantiation
h1 : true_.metaVarSet = β
β’ sub Ο Ο true_ = sub Ο Ο' true_
case not_
Ο : Instantiation
Ο Ο' : MetaInstantiation
aβ : Formula
a_ihβ : aβ.metaVarSet = β
β sub Ο Ο aβ = sub Ο Ο' aβ
h1 : aβ.not_.metaVarSet = β
β’ sub Ο Ο aβ.not_ = sub Ο Ο' aβ.not_
case imp_
Ο : Instantiation
Ο Ο' : MetaInstantiation
aβΒΉ aβ : Formula
a_ihβΒΉ : aβΒΉ.metaVarSet = β
β sub Ο Ο aβΒΉ = sub Ο Ο' aβΒΉ
a_ihβ : aβ.metaVarSet = β
β sub Ο Ο aβ = sub Ο Ο' aβ
h1 : (aβΒΉ.imp_ aβ).metaVarSet = β
β’ sub Ο Ο (aβΒΉ.imp_ aβ) = sub Ο Ο' (aβΒΉ.imp_ aβ)
case forall_
Ο : Instantiation
Ο Ο' : MetaInstantiation
aβΒΉ : VarName
aβ : Formula
a_ihβ : aβ.metaVarSet = β
β sub Ο Ο aβ = sub Ο Ο' aβ
h1 : (forall_ aβΒΉ aβ).metaVarSet = β
β’ sub Ο Ο (forall_ aβΒΉ aβ) = sub Ο Ο' (forall_ aβΒΉ aβ)
case def_
Ο : Instantiation
Ο Ο' : MetaInstantiation
aβΒΉ : DefName
aβ : List VarName
h1 : (def_ aβΒΉ aβ).metaVarSet = β
β’ sub Ο Ο (def_ aβΒΉ aβ) = sub Ο Ο' (def_ aβΒΉ aβ) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | case meta_var_ X =>
unfold Formula.metaVarSet at h1
simp at h1 | Ο : Instantiation
Ο Ο' : MetaInstantiation
X : MetaVarName
h1 : (meta_var_ X).metaVarSet = β
β’ sub Ο Ο (meta_var_ X) = sub Ο Ο' (meta_var_ X) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | case pred_ X xs =>
rfl | Ο : Instantiation
Ο Ο' : MetaInstantiation
X : PredName
xs : List VarName
h1 : (pred_ X xs).metaVarSet = β
β’ sub Ο Ο (pred_ X xs) = sub Ο Ο' (pred_ X xs) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | case eq_ x y =>
rfl | Ο : Instantiation
Ο Ο' : MetaInstantiation
x y : VarName
h1 : (eq_ x y).metaVarSet = β
β’ sub Ο Ο (eq_ x y) = sub Ο Ο' (eq_ x y) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | case true_ =>
rfl | Ο : Instantiation
Ο Ο' : MetaInstantiation
h1 : true_.metaVarSet = β
β’ sub Ο Ο true_ = sub Ο Ο' true_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | case not_ phi phi_ih =>
unfold Formula.metaVarSet at h1
unfold sub
congr! 1
exact phi_ih h1 | Ο : Instantiation
Ο Ο' : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β sub Ο Ο phi = sub Ο Ο' phi
h1 : phi.not_.metaVarSet = β
β’ sub Ο Ο phi.not_ = sub Ο Ο' phi.not_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | case forall_ x phi phi_ih =>
unfold Formula.metaVarSet at h1
unfold sub
congr! 1
exact phi_ih h1 | Ο : Instantiation
Ο Ο' : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = β
β sub Ο Ο phi = sub Ο Ο' phi
h1 : (forall_ x phi).metaVarSet = β
β’ sub Ο Ο (forall_ x phi) = sub Ο Ο' (forall_ x phi) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | case def_ X xs =>
rfl | Ο : Instantiation
Ο Ο' : MetaInstantiation
X : DefName
xs : List VarName
h1 : (def_ X xs).metaVarSet = β
β’ sub Ο Ο (def_ X xs) = sub Ο Ο' (def_ X xs) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | unfold Formula.metaVarSet at h1 | Ο : Instantiation
Ο Ο' : MetaInstantiation
X : MetaVarName
h1 : (meta_var_ X).metaVarSet = β
β’ sub Ο Ο (meta_var_ X) = sub Ο Ο' (meta_var_ X) | Ο : Instantiation
Ο Ο' : MetaInstantiation
X : MetaVarName
h1 : {X} = β
β’ sub Ο Ο (meta_var_ X) = sub Ο Ο' (meta_var_ X) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | simp at h1 | Ο : Instantiation
Ο Ο' : MetaInstantiation
X : MetaVarName
h1 : {X} = β
β’ sub Ο Ο (meta_var_ X) = sub Ο Ο' (meta_var_ X) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | rfl | Ο : Instantiation
Ο Ο' : MetaInstantiation
X : PredName
xs : List VarName
h1 : (pred_ X xs).metaVarSet = β
β’ sub Ο Ο (pred_ X xs) = sub Ο Ο' (pred_ X xs) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | rfl | Ο : Instantiation
Ο Ο' : MetaInstantiation
x y : VarName
h1 : (eq_ x y).metaVarSet = β
β’ sub Ο Ο (eq_ x y) = sub Ο Ο' (eq_ x y) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | rfl | Ο : Instantiation
Ο Ο' : MetaInstantiation
h1 : true_.metaVarSet = β
β’ sub Ο Ο true_ = sub Ο Ο' true_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | unfold Formula.metaVarSet at h1 | Ο : Instantiation
Ο Ο' : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β sub Ο Ο phi = sub Ο Ο' phi
h1 : phi.not_.metaVarSet = β
β’ sub Ο Ο phi.not_ = sub Ο Ο' phi.not_ | Ο : Instantiation
Ο Ο' : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β sub Ο Ο phi = sub Ο Ο' phi
h1 : phi.metaVarSet = β
β’ sub Ο Ο phi.not_ = sub Ο Ο' phi.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | unfold sub | Ο : Instantiation
Ο Ο' : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β sub Ο Ο phi = sub Ο Ο' phi
h1 : phi.metaVarSet = β
β’ sub Ο Ο phi.not_ = sub Ο Ο' phi.not_ | Ο : Instantiation
Ο Ο' : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β sub Ο Ο phi = sub Ο Ο' phi
h1 : phi.metaVarSet = β
β’ (sub Ο Ο phi).not_ = (sub Ο Ο' phi).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | congr! 1 | Ο : Instantiation
Ο Ο' : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β sub Ο Ο phi = sub Ο Ο' phi
h1 : phi.metaVarSet = β
β’ (sub Ο Ο phi).not_ = (sub Ο Ο' phi).not_ | case h.e'_1
Ο : Instantiation
Ο Ο' : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β sub Ο Ο phi = sub Ο Ο' phi
h1 : phi.metaVarSet = β
β’ sub Ο Ο phi = sub Ο Ο' phi |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_instantiation_irrelevance_in_sub | [820, 1] | [860, 8] | exact phi_ih h1 | case h.e'_1
Ο : Instantiation
Ο Ο' : MetaInstantiation
phi : Formula
phi_ih : phi.metaVarSet = β
β sub Ο Ο phi = sub Ο Ο' phi
h1 : phi.metaVarSet = β
β’ sub Ο Ο phi = sub Ο Ο' phi | no goals |
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