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https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | case _ a2_left a2_right =>
subst a2_right
simp only [isFree]
simp
exact a2_left | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.freeVarSet
x : String
a2_left : free_ x β vs
a2_right : v = free_ x
β’ v β vs β§ v.isFree | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | subst a2_right | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.freeVarSet
x : String
a2_left : free_ x β vs
a2_right : v = free_ x
β’ v β vs β§ v.isFree | X : String
vs : List Var
x : String
a2_left : free_ x β vs
a1 : β a β vs, free_ x β a.freeVarSet
β’ free_ x β vs β§ (free_ x).isFree |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp only [isFree] | X : String
vs : List Var
x : String
a2_left : free_ x β vs
a1 : β a β vs, free_ x β a.freeVarSet
β’ free_ x β vs β§ (free_ x).isFree | X : String
vs : List Var
x : String
a2_left : free_ x β vs
a1 : β a β vs, free_ x β a.freeVarSet
β’ free_ x β vs β§ True |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp | X : String
vs : List Var
x : String
a2_left : free_ x β vs
a1 : β a β vs, free_ x β a.freeVarSet
β’ free_ x β vs β§ True | X : String
vs : List Var
x : String
a2_left : free_ x β vs
a1 : β a β vs, free_ x β a.freeVarSet
β’ free_ x β vs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | exact a2_left | X : String
vs : List Var
x : String
a2_left : free_ x β vs
a1 : β a β vs, free_ x β a.freeVarSet
β’ free_ x β vs | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp only [Var.freeVarSet] at a2 | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.freeVarSet
i : β
a2 : bound_ i β vs β§ v β (bound_ i).freeVarSet
β’ v β vs β§ v.isFree | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.freeVarSet
i : β
a2 : bound_ i β vs β§ v β β
β’ v β vs β§ v.isFree |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp at a2 | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.freeVarSet
i : β
a2 : bound_ i β vs β§ v β β
β’ v β vs β§ v.isFree | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp only [Formula.freeVarSet] | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
β’ occursIn v phi.not_ β§ v.isFree β v β phi.not_.freeVarSet | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
β’ occursIn v phi.not_ β§ v.isFree β v β phi.freeVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp only [occursIn] | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
β’ occursIn v phi.not_ β§ v.isFree β v β phi.freeVarSet | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
β’ occursIn v phi β§ v.isFree β v β phi.freeVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | exact phi_ih | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
β’ occursIn v phi β§ v.isFree β v β phi.freeVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp only [Formula.freeVarSet] | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
psi_ih : occursIn v psi β§ v.isFree β v β psi.freeVarSet
β’ occursIn v (phi.imp_ psi) β§ v.isFree β v β (phi.imp_ psi).freeVarSet | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
psi_ih : occursIn v psi β§ v.isFree β v β psi.freeVarSet
β’ occursIn v (phi.imp_ psi) β§ v.isFree β v β phi.freeVarSet βͺ psi.freeVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp only [occursIn] | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
psi_ih : occursIn v psi β§ v.isFree β v β psi.freeVarSet
β’ occursIn v (phi.imp_ psi) β§ v.isFree β v β phi.freeVarSet βͺ psi.freeVarSet | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
psi_ih : occursIn v psi β§ v.isFree β v β psi.freeVarSet
β’ (occursIn v phi β¨ occursIn v psi) β§ v.isFree β v β phi.freeVarSet βͺ psi.freeVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
psi_ih : occursIn v psi β§ v.isFree β v β psi.freeVarSet
β’ (occursIn v phi β¨ occursIn v psi) β§ v.isFree β v β phi.freeVarSet βͺ psi.freeVarSet | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
psi_ih : occursIn v psi β§ v.isFree β v β psi.freeVarSet
β’ (occursIn v phi β¨ occursIn v psi) β§ v.isFree β v β phi.freeVarSet β¨ v β psi.freeVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | tauto | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
psi_ih : occursIn v psi β§ v.isFree β v β psi.freeVarSet
β’ (occursIn v phi β¨ occursIn v psi) β§ v.isFree β v β phi.freeVarSet β¨ v β psi.freeVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp only [Formula.freeVarSet] | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
β’ occursIn v (forall_ aβ phi) β§ v.isFree β v β (forall_ aβ phi).freeVarSet | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
β’ occursIn v (forall_ aβ phi) β§ v.isFree β v β phi.freeVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | simp only [occursIn] | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
β’ occursIn v (forall_ aβ phi) β§ v.isFree β v β phi.freeVarSet | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
β’ occursIn v phi β§ v.isFree β v β phi.freeVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet | [211, 1] | [264, 17] | exact phi_ih | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isFree β v β phi.freeVarSet
β’ occursIn v phi β§ v.isFree β v β phi.freeVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | induction F | v : Var
F : Formula
β’ occursIn v F β§ v.isBound β v β F.boundVarSet | case pred_
v : Var
aβΒΉ : String
aβ : List Var
β’ occursIn v (pred_ aβΒΉ aβ) β§ v.isBound β v β (pred_ aβΒΉ aβ).boundVarSet
case not_
v : Var
aβ : Formula
a_ihβ : occursIn v aβ β§ v.isBound β v β aβ.boundVarSet
β’ occursIn v aβ.not_ β§ v.isBound β v β aβ.not_.boundVarSet
case imp_
v : Var
aβΒΉ aβ : Formula
a_ihβΒΉ : occursIn v aβΒΉ β§ v.isBound β v β aβΒΉ.boundVarSet
a_ihβ : occursIn v aβ β§ v.isBound β v β aβ.boundVarSet
β’ occursIn v (aβΒΉ.imp_ aβ) β§ v.isBound β v β (aβΒΉ.imp_ aβ).boundVarSet
case forall_
v : Var
aβΒΉ : String
aβ : Formula
a_ihβ : occursIn v aβ β§ v.isBound β v β aβ.boundVarSet
β’ occursIn v (forall_ aβΒΉ aβ) β§ v.isBound β v β (forall_ aβΒΉ aβ).boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | case not_ phi phi_ih =>
simp only [Formula.boundVarSet]
simp only [occursIn]
exact phi_ih | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v phi.not_ β§ v.isBound β v β phi.not_.boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | case imp_ phi psi phi_ih psi_ih =>
simp only [Formula.boundVarSet]
simp only [occursIn]
simp
tauto | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
psi_ih : occursIn v psi β§ v.isBound β v β psi.boundVarSet
β’ occursIn v (phi.imp_ psi) β§ v.isBound β v β (phi.imp_ psi).boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | case forall_ _ phi phi_ih =>
simp only [Formula.boundVarSet]
simp only [occursIn]
exact phi_ih | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v (forall_ aβ phi) β§ v.isBound β v β (forall_ aβ phi).boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [Formula.boundVarSet] | v : Var
X : String
vs : List Var
β’ occursIn v (pred_ X vs) β§ v.isBound β v β (pred_ X vs).boundVarSet | v : Var
X : String
vs : List Var
β’ occursIn v (pred_ X vs) β§ v.isBound β v β vs.toFinset.biUnion Var.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [occursIn] | v : Var
X : String
vs : List Var
β’ occursIn v (pred_ X vs) β§ v.isBound β v β vs.toFinset.biUnion Var.boundVarSet | v : Var
X : String
vs : List Var
β’ v β vs β§ v.isBound β v β vs.toFinset.biUnion Var.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp | v : Var
X : String
vs : List Var
β’ v β vs β§ v.isBound β v β vs.toFinset.biUnion Var.boundVarSet | v : Var
X : String
vs : List Var
β’ v β vs β§ v.isBound β β a β vs, v β a.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | constructor | v : Var
X : String
vs : List Var
β’ v β vs β§ v.isBound β β a β vs, v β a.boundVarSet | case mp
v : Var
X : String
vs : List Var
β’ v β vs β§ v.isBound β β a β vs, v β a.boundVarSet
case mpr
v : Var
X : String
vs : List Var
β’ (β a β vs, v β a.boundVarSet) β v β vs β§ v.isBound |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | intro a1 | case mp
v : Var
X : String
vs : List Var
β’ v β vs β§ v.isBound β β a β vs, v β a.boundVarSet | case mp
v : Var
X : String
vs : List Var
a1 : v β vs β§ v.isBound
β’ β a β vs, v β a.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | apply Exists.intro v | case mp
v : Var
X : String
vs : List Var
a1 : v β vs β§ v.isBound
β’ β a β vs, v β a.boundVarSet | case mp
v : Var
X : String
vs : List Var
a1 : v β vs β§ v.isBound
β’ v β vs β§ v β v.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | cases v | case mp
v : Var
X : String
vs : List Var
a1 : v β vs β§ v.isBound
β’ v β vs β§ v β v.boundVarSet | case mp.free_
X : String
vs : List Var
aβ : String
a1 : free_ aβ β vs β§ (free_ aβ).isBound
β’ free_ aβ β vs β§ free_ aβ β (free_ aβ).boundVarSet
case mp.bound_
X : String
vs : List Var
aβ : β
a1 : bound_ aβ β vs β§ (bound_ aβ).isBound
β’ bound_ aβ β vs β§ bound_ aβ β (bound_ aβ).boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | case _ x =>
simp only [Var.isBound] at a1
cases a1
case _ a1_left a1_right =>
contradiction | X : String
vs : List Var
x : String
a1 : free_ x β vs β§ (free_ x).isBound
β’ free_ x β vs β§ free_ x β (free_ x).boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | case _ i =>
simp only [Var.boundVarSet]
simp
cases a1
case _ a1_left a1_right =>
exact a1_left | X : String
vs : List Var
i : β
a1 : bound_ i β vs β§ (bound_ i).isBound
β’ bound_ i β vs β§ bound_ i β (bound_ i).boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [Var.isBound] at a1 | X : String
vs : List Var
x : String
a1 : free_ x β vs β§ (free_ x).isBound
β’ free_ x β vs β§ free_ x β (free_ x).boundVarSet | X : String
vs : List Var
x : String
a1 : free_ x β vs β§ False
β’ free_ x β vs β§ free_ x β (free_ x).boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | cases a1 | X : String
vs : List Var
x : String
a1 : free_ x β vs β§ False
β’ free_ x β vs β§ free_ x β (free_ x).boundVarSet | case intro
X : String
vs : List Var
x : String
leftβ : free_ x β vs
rightβ : False
β’ free_ x β vs β§ free_ x β (free_ x).boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | case _ a1_left a1_right =>
contradiction | X : String
vs : List Var
x : String
a1_left : free_ x β vs
a1_right : False
β’ free_ x β vs β§ free_ x β (free_ x).boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | contradiction | X : String
vs : List Var
x : String
a1_left : free_ x β vs
a1_right : False
β’ free_ x β vs β§ free_ x β (free_ x).boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [Var.boundVarSet] | X : String
vs : List Var
i : β
a1 : bound_ i β vs β§ (bound_ i).isBound
β’ bound_ i β vs β§ bound_ i β (bound_ i).boundVarSet | X : String
vs : List Var
i : β
a1 : bound_ i β vs β§ (bound_ i).isBound
β’ bound_ i β vs β§ bound_ i β {bound_ i} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp | X : String
vs : List Var
i : β
a1 : bound_ i β vs β§ (bound_ i).isBound
β’ bound_ i β vs β§ bound_ i β {bound_ i} | X : String
vs : List Var
i : β
a1 : bound_ i β vs β§ (bound_ i).isBound
β’ bound_ i β vs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | cases a1 | X : String
vs : List Var
i : β
a1 : bound_ i β vs β§ (bound_ i).isBound
β’ bound_ i β vs | case intro
X : String
vs : List Var
i : β
leftβ : bound_ i β vs
rightβ : (bound_ i).isBound
β’ bound_ i β vs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | case _ a1_left a1_right =>
exact a1_left | X : String
vs : List Var
i : β
a1_left : bound_ i β vs
a1_right : (bound_ i).isBound
β’ bound_ i β vs | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | exact a1_left | X : String
vs : List Var
i : β
a1_left : bound_ i β vs
a1_right : (bound_ i).isBound
β’ bound_ i β vs | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | intro a1 | case mpr
v : Var
X : String
vs : List Var
β’ (β a β vs, v β a.boundVarSet) β v β vs β§ v.isBound | case mpr
v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
β’ v β vs β§ v.isBound |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | apply Exists.elim a1 | case mpr
v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
β’ v β vs β§ v.isBound | case mpr
v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
β’ β (a : Var), a β vs β§ v β a.boundVarSet β v β vs β§ v.isBound |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | intro u a2 | case mpr
v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
β’ β (a : Var), a β vs β§ v β a.boundVarSet β v β vs β§ v.isBound | case mpr
v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
u : Var
a2 : u β vs β§ v β u.boundVarSet
β’ v β vs β§ v.isBound |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | cases u | case mpr
v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
u : Var
a2 : u β vs β§ v β u.boundVarSet
β’ v β vs β§ v.isBound | case mpr.free_
v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
aβ : String
a2 : free_ aβ β vs β§ v β (free_ aβ).boundVarSet
β’ v β vs β§ v.isBound
case mpr.bound_
v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
aβ : β
a2 : bound_ aβ β vs β§ v β (bound_ aβ).boundVarSet
β’ v β vs β§ v.isBound |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | case _ x =>
simp only [Var.boundVarSet] at a2
simp at a2 | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
x : String
a2 : free_ x β vs β§ v β (free_ x).boundVarSet
β’ v β vs β§ v.isBound | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | case _ i =>
simp only [Var.boundVarSet] at a2
simp at a2
cases a2
case _ a2_left a2_right =>
subst a2_right
simp only [isBound]
simp
exact a2_left | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
i : β
a2 : bound_ i β vs β§ v β (bound_ i).boundVarSet
β’ v β vs β§ v.isBound | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [Var.boundVarSet] at a2 | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
x : String
a2 : free_ x β vs β§ v β (free_ x).boundVarSet
β’ v β vs β§ v.isBound | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
x : String
a2 : free_ x β vs β§ v β β
β’ v β vs β§ v.isBound |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp at a2 | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
x : String
a2 : free_ x β vs β§ v β β
β’ v β vs β§ v.isBound | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [Var.boundVarSet] at a2 | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
i : β
a2 : bound_ i β vs β§ v β (bound_ i).boundVarSet
β’ v β vs β§ v.isBound | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
i : β
a2 : bound_ i β vs β§ v β {bound_ i}
β’ v β vs β§ v.isBound |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp at a2 | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
i : β
a2 : bound_ i β vs β§ v β {bound_ i}
β’ v β vs β§ v.isBound | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
i : β
a2 : bound_ i β vs β§ v = bound_ i
β’ v β vs β§ v.isBound |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | cases a2 | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
i : β
a2 : bound_ i β vs β§ v = bound_ i
β’ v β vs β§ v.isBound | case intro
v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
i : β
leftβ : bound_ i β vs
rightβ : v = bound_ i
β’ v β vs β§ v.isBound |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | case _ a2_left a2_right =>
subst a2_right
simp only [isBound]
simp
exact a2_left | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
i : β
a2_left : bound_ i β vs
a2_right : v = bound_ i
β’ v β vs β§ v.isBound | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | subst a2_right | v : Var
X : String
vs : List Var
a1 : β a β vs, v β a.boundVarSet
i : β
a2_left : bound_ i β vs
a2_right : v = bound_ i
β’ v β vs β§ v.isBound | X : String
vs : List Var
i : β
a2_left : bound_ i β vs
a1 : β a β vs, bound_ i β a.boundVarSet
β’ bound_ i β vs β§ (bound_ i).isBound |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [isBound] | X : String
vs : List Var
i : β
a2_left : bound_ i β vs
a1 : β a β vs, bound_ i β a.boundVarSet
β’ bound_ i β vs β§ (bound_ i).isBound | X : String
vs : List Var
i : β
a2_left : bound_ i β vs
a1 : β a β vs, bound_ i β a.boundVarSet
β’ bound_ i β vs β§ True |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp | X : String
vs : List Var
i : β
a2_left : bound_ i β vs
a1 : β a β vs, bound_ i β a.boundVarSet
β’ bound_ i β vs β§ True | X : String
vs : List Var
i : β
a2_left : bound_ i β vs
a1 : β a β vs, bound_ i β a.boundVarSet
β’ bound_ i β vs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | exact a2_left | X : String
vs : List Var
i : β
a2_left : bound_ i β vs
a1 : β a β vs, bound_ i β a.boundVarSet
β’ bound_ i β vs | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [Formula.boundVarSet] | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v phi.not_ β§ v.isBound β v β phi.not_.boundVarSet | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v phi.not_ β§ v.isBound β v β phi.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [occursIn] | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v phi.not_ β§ v.isBound β v β phi.boundVarSet | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v phi β§ v.isBound β v β phi.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | exact phi_ih | v : Var
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v phi β§ v.isBound β v β phi.boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [Formula.boundVarSet] | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
psi_ih : occursIn v psi β§ v.isBound β v β psi.boundVarSet
β’ occursIn v (phi.imp_ psi) β§ v.isBound β v β (phi.imp_ psi).boundVarSet | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
psi_ih : occursIn v psi β§ v.isBound β v β psi.boundVarSet
β’ occursIn v (phi.imp_ psi) β§ v.isBound β v β phi.boundVarSet βͺ psi.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [occursIn] | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
psi_ih : occursIn v psi β§ v.isBound β v β psi.boundVarSet
β’ occursIn v (phi.imp_ psi) β§ v.isBound β v β phi.boundVarSet βͺ psi.boundVarSet | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
psi_ih : occursIn v psi β§ v.isBound β v β psi.boundVarSet
β’ (occursIn v phi β¨ occursIn v psi) β§ v.isBound β v β phi.boundVarSet βͺ psi.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
psi_ih : occursIn v psi β§ v.isBound β v β psi.boundVarSet
β’ (occursIn v phi β¨ occursIn v psi) β§ v.isBound β v β phi.boundVarSet βͺ psi.boundVarSet | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
psi_ih : occursIn v psi β§ v.isBound β v β psi.boundVarSet
β’ (occursIn v phi β¨ occursIn v psi) β§ v.isBound β v β phi.boundVarSet β¨ v β psi.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | tauto | v : Var
phi psi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
psi_ih : occursIn v psi β§ v.isBound β v β psi.boundVarSet
β’ (occursIn v phi β¨ occursIn v psi) β§ v.isBound β v β phi.boundVarSet β¨ v β psi.boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [Formula.boundVarSet] | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v (forall_ aβ phi) β§ v.isBound β v β (forall_ aβ phi).boundVarSet | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v (forall_ aβ phi) β§ v.isBound β v β phi.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | simp only [occursIn] | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v (forall_ aβ phi) β§ v.isBound β v β phi.boundVarSet | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v phi β§ v.isBound β v β phi.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet | [267, 1] | [320, 17] | exact phi_ih | v : Var
aβ : String
phi : Formula
phi_ih : occursIn v phi β§ v.isBound β v β phi.boundVarSet
β’ occursIn v phi β§ v.isBound β v β phi.boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet' | [323, 1] | [331, 36] | simp only [freeVarSet'] | v : Var
F : Formula
β’ occursIn v F β§ v.isFree β v β F.freeVarSet' | v : Var
F : Formula
β’ occursIn v F β§ v.isFree β v β Finset.filter isFree F.varSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet' | [323, 1] | [331, 36] | simp | v : Var
F : Formula
β’ occursIn v F β§ v.isFree β v β Finset.filter isFree F.varSet | v : Var
F : Formula
β’ v.isFree β (occursIn v F β v β F.varSet) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet' | [323, 1] | [331, 36] | intro _ | v : Var
F : Formula
β’ v.isFree β (occursIn v F β v β F.varSet) | v : Var
F : Formula
aβ : v.isFree
β’ occursIn v F β v β F.varSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isFreeIn_iff_mem_freeVarSet' | [323, 1] | [331, 36] | exact occursIn_iff_mem_varSet v F | v : Var
F : Formula
aβ : v.isFree
β’ occursIn v F β v β F.varSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet' | [334, 1] | [342, 36] | simp only [boundVarSet'] | v : Var
F : Formula
β’ occursIn v F β§ v.isBound β v β F.boundVarSet' | v : Var
F : Formula
β’ occursIn v F β§ v.isBound β v β Finset.filter isBound F.varSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet' | [334, 1] | [342, 36] | simp | v : Var
F : Formula
β’ occursIn v F β§ v.isBound β v β Finset.filter isBound F.varSet | v : Var
F : Formula
β’ v.isBound β (occursIn v F β v β F.varSet) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet' | [334, 1] | [342, 36] | intro _ | v : Var
F : Formula
β’ v.isBound β (occursIn v F β v β F.varSet) | v : Var
F : Formula
aβ : v.isBound
β’ occursIn v F β v β F.varSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.isBoundIn_iff_mem_boundVarSet' | [334, 1] | [342, 36] | exact occursIn_iff_mem_varSet v F | v : Var
F : Formula
aβ : v.isBound
β’ occursIn v F β v β F.varSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.IsFreeIffExistsString | [346, 1] | [356, 9] | cases v | v : Var
β’ v.isFree β β x, v = free_ x | case free_
aβ : String
β’ (free_ aβ).isFree β β x, free_ aβ = free_ x
case bound_
aβ : β
β’ (bound_ aβ).isFree β β x, bound_ aβ = free_ x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.IsFreeIffExistsString | [346, 1] | [356, 9] | case free_ x =>
simp only [isFree]
simp | x : String
β’ (free_ x).isFree β β x_1, free_ x = free_ x_1 | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.IsFreeIffExistsString | [346, 1] | [356, 9] | case bound_ i =>
simp only [isFree]
simp | i : β
β’ (bound_ i).isFree β β x, bound_ i = free_ x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.IsFreeIffExistsString | [346, 1] | [356, 9] | simp only [isFree] | x : String
β’ (free_ x).isFree β β x_1, free_ x = free_ x_1 | x : String
β’ True β β x_1, free_ x = free_ x_1 |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.IsFreeIffExistsString | [346, 1] | [356, 9] | simp | x : String
β’ True β β x_1, free_ x = free_ x_1 | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.IsFreeIffExistsString | [346, 1] | [356, 9] | simp only [isFree] | i : β
β’ (bound_ i).isFree β β x, bound_ i = free_ x | i : β
β’ False β β x, False |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Binders.lean | LN.IsFreeIffExistsString | [346, 1] | [356, 9] | simp | i : β
β’ False β β x, False | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFA.lean | DFA.mem_accepts | [91, 1] | [99, 74] | rfl | Ξ± : Type
instβΒΉ : DecidableEq Ξ±
Ο : Type
instβ : DecidableEq Ο
D : DFA Ξ± Ο
input : List Ξ±
β’ D.accepts input β D.eval_from D.starting_state input β D.accepting_state_list | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFA.lean | NFA_to_DFA_is_equiv | [105, 1] | [117, 8] | ext cs | Ξ± : Type
instβΒΉ : DecidableEq Ξ±
Ο : Type
instβ : DecidableEq Ο
N : NFA Ξ± Ο
β’ N.to_DFA.accepts = N.accepts | case h.a
Ξ± : Type
instβΒΉ : DecidableEq Ξ±
Ο : Type
instβ : DecidableEq Ο
N : NFA Ξ± Ο
cs : List Ξ±
β’ N.to_DFA.accepts cs β N.accepts cs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFA.lean | NFA_to_DFA_is_equiv | [105, 1] | [117, 8] | simp only [DFA.mem_accepts] | case h.a
Ξ± : Type
instβΒΉ : DecidableEq Ξ±
Ο : Type
instβ : DecidableEq Ο
N : NFA Ξ± Ο
cs : List Ξ±
β’ N.to_DFA.accepts cs β N.accepts cs | case h.a
Ξ± : Type
instβΒΉ : DecidableEq Ξ±
Ο : Type
instβ : DecidableEq Ο
N : NFA Ξ± Ο
cs : List Ξ±
β’ N.to_DFA.eval_from N.to_DFA.starting_state cs β N.to_DFA.accepting_state_list β N.accepts cs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFA.lean | NFA_to_DFA_is_equiv | [105, 1] | [117, 8] | simp only [NFA.mem_accepts] | case h.a
Ξ± : Type
instβΒΉ : DecidableEq Ξ±
Ο : Type
instβ : DecidableEq Ο
N : NFA Ξ± Ο
cs : List Ξ±
β’ N.to_DFA.eval_from N.to_DFA.starting_state cs β N.to_DFA.accepting_state_list β N.accepts cs | case h.a
Ξ± : Type
instβΒΉ : DecidableEq Ξ±
Ο : Type
instβ : DecidableEq Ο
N : NFA Ξ± Ο
cs : List Ξ±
β’ N.to_DFA.eval_from N.to_DFA.starting_state cs β N.to_DFA.accepting_state_list β
β s β N.eval_from N.starting_state_list cs, s β N.accepting_state_list |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFA.lean | NFA_to_DFA_is_equiv | [105, 1] | [117, 8] | simp only [NFA.to_DFA] | case h.a
Ξ± : Type
instβΒΉ : DecidableEq Ξ±
Ο : Type
instβ : DecidableEq Ο
N : NFA Ξ± Ο
cs : List Ξ±
β’ N.to_DFA.eval_from N.to_DFA.starting_state cs β N.to_DFA.accepting_state_list β
β s β N.eval_from N.starting_state_list cs, s β N.accepting_state_list | case h.a
Ξ± : Type
instβΒΉ : DecidableEq Ξ±
Ο : Type
instβ : DecidableEq Ο
N : NFA Ξ± Ο
cs : List Ξ±
β’ { step := N.eval_one, starting_state := N.starting_state_list,
accepting_state_list := sorryAx (List (List Ο)) }.eval_from
N.starting_state_list cs β
sorryAx (List (List Ο)) β
β s β N.eval_from N.starting_state_list cs, s β N.accepting_state_list |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFA.lean | NFA_to_DFA_is_equiv | [105, 1] | [117, 8] | sorry | case h.a
Ξ± : Type
instβΒΉ : DecidableEq Ξ±
Ο : Type
instβ : DecidableEq Ο
N : NFA Ξ± Ο
cs : List Ξ±
β’ { step := N.eval_one, starting_state := N.starting_state_list,
accepting_state_list := sorryAx (List (List Ο)) }.eval_from
N.starting_state_list cs β
sorryAx (List (List Ο)) β
β s β N.eval_from N.starting_state_list cs, s β N.accepting_state_list | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationEmpty | [208, 1] | [218, 7] | cases h1 | V_N V_T : Type
R : V_N β PE V_N V_T
n : β
xs : List V_T
o : Option (List V_T)
h1 : Interpretation V_N V_T R (empty, xs) (n, o)
β’ n = 1 β§ o = some [] | case empty
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
β’ 1 = 1 β§ some [] = some [] |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationEmpty | [208, 1] | [218, 7] | simp | case empty
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
β’ 1 = 1 β§ some [] = some [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationSteps | [221, 1] | [233, 10] | cases h1 | V_N V_T : Type
R : V_N β PE V_N V_T
e : PE V_N V_T
xs : List V_T
o : Option (List V_T)
n : β
h1 : Interpretation V_N V_T R (e, xs) (n, o)
β’ n > 0 | case empty
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
β’ 1 > 0
case terminal_success
V_N V_T : Type
R : V_N β PE V_N V_T
aβ : V_T
xsβ : List V_T
β’ 1 > 0
case terminal_failure_1
V_N V_T : Type
R : V_N β PE V_N V_T
aβΒΉ bβ : V_T
xsβ : List V_T
aβ : Β¬aβΒΉ = bβ
β’ 1 > 0
case terminal_failure_2
V_N V_T : Type
R : V_N β PE V_N V_T
aβ : V_T
xsβ : List V_T
β’ 1 > 0
case nonTerminal
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
o : Option (List V_T)
Aβ : V_N
nβ : β
aβ : Interpretation V_N V_T R (R Aβ, xs) (nβ, o)
β’ nβ + 1 > 0
case seq_success
V_N V_T : Type
R : V_N β PE V_N V_T
e1β e2β : PE V_N V_T
xs_1β xs_2β ysβ : List V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xs_1β ++ xs_2β ++ ysβ) (n1β, some xs_1β)
aβ : Interpretation V_N V_T R (e2β, xs_2β ++ ysβ) (n2β, some xs_2β)
β’ n1β + n2β + 1 > 0
case seq_failure_1
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
e1β e2β : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (e1β, xs) (nβ, none)
β’ nβ + 1 > 0
case seq_failure_2
V_N V_T : Type
R : V_N β PE V_N V_T
e1β e2β : PE V_N V_T
xsβ ysβ : List V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xsβ ++ ysβ) (n1β, some xsβ)
aβ : Interpretation V_N V_T R (e2β, ysβ) (n2β, none)
β’ n1β + n2β + 1 > 0
case choice_1
V_N V_T : Type
R : V_N β PE V_N V_T
e1β e2β : PE V_N V_T
xsβ ysβ : List V_T
nβ : β
aβ : Interpretation V_N V_T R (e1β, xsβ ++ ysβ) (nβ, some xsβ)
β’ nβ + 1 > 0
case choice_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
o : Option (List V_T)
e1β e2β : PE V_N V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xs) (n1β, none)
aβ : Interpretation V_N V_T R (e2β, xs) (n2β, o)
β’ n1β + n2β + 1 > 0
case star_repetition
V_N V_T : Type
R : V_N β PE V_N V_T
eβ : PE V_N V_T
xs_1β xs_2β ysβ : List V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (eβ, xs_1β ++ xs_2β ++ ysβ) (n1β, some xs_1β)
aβ : Interpretation V_N V_T R (eβ.star, xs_2β ++ ysβ) (n2β, some xs_2β)
β’ n1β + n2β + 1 > 0
case star_termination
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
β’ nβ + 1 > 0
case notP_1
V_N V_T : Type
R : V_N β PE V_N V_T
eβ : PE V_N V_T
xsβ ysβ : List V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xsβ ++ ysβ) (nβ, some xsβ)
β’ nβ + 1 > 0
case notP_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
β’ nβ + 1 > 0 |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationSteps | [221, 1] | [233, 10] | all_goals
omega | case empty
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
β’ 1 > 0
case terminal_success
V_N V_T : Type
R : V_N β PE V_N V_T
aβ : V_T
xsβ : List V_T
β’ 1 > 0
case terminal_failure_1
V_N V_T : Type
R : V_N β PE V_N V_T
aβΒΉ bβ : V_T
xsβ : List V_T
aβ : Β¬aβΒΉ = bβ
β’ 1 > 0
case terminal_failure_2
V_N V_T : Type
R : V_N β PE V_N V_T
aβ : V_T
xsβ : List V_T
β’ 1 > 0
case nonTerminal
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
o : Option (List V_T)
Aβ : V_N
nβ : β
aβ : Interpretation V_N V_T R (R Aβ, xs) (nβ, o)
β’ nβ + 1 > 0
case seq_success
V_N V_T : Type
R : V_N β PE V_N V_T
e1β e2β : PE V_N V_T
xs_1β xs_2β ysβ : List V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xs_1β ++ xs_2β ++ ysβ) (n1β, some xs_1β)
aβ : Interpretation V_N V_T R (e2β, xs_2β ++ ysβ) (n2β, some xs_2β)
β’ n1β + n2β + 1 > 0
case seq_failure_1
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
e1β e2β : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (e1β, xs) (nβ, none)
β’ nβ + 1 > 0
case seq_failure_2
V_N V_T : Type
R : V_N β PE V_N V_T
e1β e2β : PE V_N V_T
xsβ ysβ : List V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xsβ ++ ysβ) (n1β, some xsβ)
aβ : Interpretation V_N V_T R (e2β, ysβ) (n2β, none)
β’ n1β + n2β + 1 > 0
case choice_1
V_N V_T : Type
R : V_N β PE V_N V_T
e1β e2β : PE V_N V_T
xsβ ysβ : List V_T
nβ : β
aβ : Interpretation V_N V_T R (e1β, xsβ ++ ysβ) (nβ, some xsβ)
β’ nβ + 1 > 0
case choice_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
o : Option (List V_T)
e1β e2β : PE V_N V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xs) (n1β, none)
aβ : Interpretation V_N V_T R (e2β, xs) (n2β, o)
β’ n1β + n2β + 1 > 0
case star_repetition
V_N V_T : Type
R : V_N β PE V_N V_T
eβ : PE V_N V_T
xs_1β xs_2β ysβ : List V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (eβ, xs_1β ++ xs_2β ++ ysβ) (n1β, some xs_1β)
aβ : Interpretation V_N V_T R (eβ.star, xs_2β ++ ysβ) (n2β, some xs_2β)
β’ n1β + n2β + 1 > 0
case star_termination
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
β’ nβ + 1 > 0
case notP_1
V_N V_T : Type
R : V_N β PE V_N V_T
eβ : PE V_N V_T
xsβ ysβ : List V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xsβ ++ ysβ) (nβ, some xsβ)
β’ nβ + 1 > 0
case notP_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
β’ nβ + 1 > 0 | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationSteps | [221, 1] | [233, 10] | omega | case notP_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
β’ nβ + 1 > 0 | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | EmptyStringPrefix | [236, 1] | [241, 27] | exact List.nil_prefix xs | Ξ± : Type
xs : List Ξ±
β’ [].IsPrefix xs | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | CharPrefix | [244, 1] | [250, 40] | exact List.prefix_iff_eq_take.mpr rfl | Ξ± : Type
x : Ξ±
xs : List Ξ±
β’ [x].IsPrefix (x :: xs) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | PrefixAppend | [253, 1] | [258, 33] | exact List.prefix_append xs ys | Ξ± : Type
xs ys : List Ξ±
β’ xs.IsPrefix (xs ++ ys) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationPrefix | [264, 1] | [285, 20] | induction n using Nat.strongInductionOn generalizing e | V_N V_T : Type
R : V_N β PE V_N V_T
e : PE V_N V_T
xs ys : List V_T
n : β
h1 : Interpretation V_N V_T R (e, xs) (n, some ys)
β’ ys.IsPrefix xs | case ind
V_N V_T : Type
R : V_N β PE V_N V_T
xs ys : List V_T
nβ : β
aβ : β m < nβ, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some ys) β ys.IsPrefix xs
e : PE V_N V_T
h1 : Interpretation V_N V_T R (e, xs) (nβ, some ys)
β’ ys.IsPrefix xs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationPrefix | [264, 1] | [285, 20] | cases h1 | V_N V_T : Type
R : V_N β PE V_N V_T
xs ys : List V_T
n : β
ih : β m < n, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some ys) β ys.IsPrefix xs
e : PE V_N V_T
h1 : Interpretation V_N V_T R (e, xs) (n, some ys)
β’ ys.IsPrefix xs | case empty
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
ih : β m < 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some []) β [].IsPrefix xs
β’ [].IsPrefix xs
case terminal_success
V_N V_T : Type
R : V_N β PE V_N V_T
aβ : V_T
xsβ : List V_T
ih : β m < 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, aβ :: xsβ) (m, some [aβ]) β [aβ].IsPrefix (aβ :: xsβ)
β’ [aβ].IsPrefix (aβ :: xsβ)
case nonTerminal
V_N V_T : Type
R : V_N β PE V_N V_T
xs ys : List V_T
Aβ : V_N
nβ : β
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some ys) β ys.IsPrefix xs
aβ : Interpretation V_N V_T R (R Aβ, xs) (nβ, some ys)
β’ ys.IsPrefix xs
case seq_success
V_N V_T : Type
R : V_N β PE V_N V_T
e1β e2β : PE V_N V_T
xs_1β xs_2β ysβ : List V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xs_1β ++ xs_2β ++ ysβ) (n1β, some xs_1β)
aβ : Interpretation V_N V_T R (e2β, xs_2β ++ ysβ) (n2β, some xs_2β)
ih :
β m < n1β + n2β + 1,
β (e : PE V_N V_T),
Interpretation V_N V_T R (e, xs_1β ++ xs_2β ++ ysβ) (m, some (xs_1β ++ xs_2β)) β
(xs_1β ++ xs_2β).IsPrefix (xs_1β ++ xs_2β ++ ysβ)
β’ (xs_1β ++ xs_2β).IsPrefix (xs_1β ++ xs_2β ++ ysβ)
case choice_1
V_N V_T : Type
R : V_N β PE V_N V_T
ys : List V_T
e1β e2β : PE V_N V_T
ysβ : List V_T
nβ : β
aβ : Interpretation V_N V_T R (e1β, ys ++ ysβ) (nβ, some ys)
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, ys ++ ysβ) (m, some ys) β ys.IsPrefix (ys ++ ysβ)
β’ ys.IsPrefix (ys ++ ysβ)
case choice_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs ys : List V_T
e1β e2β : PE V_N V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xs) (n1β, none)
ih : β m < n1β + n2β + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some ys) β ys.IsPrefix xs
aβ : Interpretation V_N V_T R (e2β, xs) (n2β, some ys)
β’ ys.IsPrefix xs
case star_repetition
V_N V_T : Type
R : V_N β PE V_N V_T
eβ : PE V_N V_T
xs_1β xs_2β ysβ : List V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (eβ, xs_1β ++ xs_2β ++ ysβ) (n1β, some xs_1β)
aβ : Interpretation V_N V_T R (eβ.star, xs_2β ++ ysβ) (n2β, some xs_2β)
ih :
β m < n1β + n2β + 1,
β (e : PE V_N V_T),
Interpretation V_N V_T R (e, xs_1β ++ xs_2β ++ ysβ) (m, some (xs_1β ++ xs_2β)) β
(xs_1β ++ xs_2β).IsPrefix (xs_1β ++ xs_2β ++ ysβ)
β’ (xs_1β ++ xs_2β).IsPrefix (xs_1β ++ xs_2β ++ ysβ)
case star_termination
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some []) β [].IsPrefix xs
β’ [].IsPrefix xs
case notP_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some []) β [].IsPrefix xs
β’ [].IsPrefix xs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationPrefix | [264, 1] | [285, 20] | any_goals
first | apply EmptyStringPrefix | apply CharPrefix | apply PrefixAppend | case empty
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
ih : β m < 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some []) β [].IsPrefix xs
β’ [].IsPrefix xs
case terminal_success
V_N V_T : Type
R : V_N β PE V_N V_T
aβ : V_T
xsβ : List V_T
ih : β m < 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, aβ :: xsβ) (m, some [aβ]) β [aβ].IsPrefix (aβ :: xsβ)
β’ [aβ].IsPrefix (aβ :: xsβ)
case nonTerminal
V_N V_T : Type
R : V_N β PE V_N V_T
xs ys : List V_T
Aβ : V_N
nβ : β
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some ys) β ys.IsPrefix xs
aβ : Interpretation V_N V_T R (R Aβ, xs) (nβ, some ys)
β’ ys.IsPrefix xs
case seq_success
V_N V_T : Type
R : V_N β PE V_N V_T
e1β e2β : PE V_N V_T
xs_1β xs_2β ysβ : List V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xs_1β ++ xs_2β ++ ysβ) (n1β, some xs_1β)
aβ : Interpretation V_N V_T R (e2β, xs_2β ++ ysβ) (n2β, some xs_2β)
ih :
β m < n1β + n2β + 1,
β (e : PE V_N V_T),
Interpretation V_N V_T R (e, xs_1β ++ xs_2β ++ ysβ) (m, some (xs_1β ++ xs_2β)) β
(xs_1β ++ xs_2β).IsPrefix (xs_1β ++ xs_2β ++ ysβ)
β’ (xs_1β ++ xs_2β).IsPrefix (xs_1β ++ xs_2β ++ ysβ)
case choice_1
V_N V_T : Type
R : V_N β PE V_N V_T
ys : List V_T
e1β e2β : PE V_N V_T
ysβ : List V_T
nβ : β
aβ : Interpretation V_N V_T R (e1β, ys ++ ysβ) (nβ, some ys)
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, ys ++ ysβ) (m, some ys) β ys.IsPrefix (ys ++ ysβ)
β’ ys.IsPrefix (ys ++ ysβ)
case choice_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs ys : List V_T
e1β e2β : PE V_N V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xs) (n1β, none)
ih : β m < n1β + n2β + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some ys) β ys.IsPrefix xs
aβ : Interpretation V_N V_T R (e2β, xs) (n2β, some ys)
β’ ys.IsPrefix xs
case star_repetition
V_N V_T : Type
R : V_N β PE V_N V_T
eβ : PE V_N V_T
xs_1β xs_2β ysβ : List V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (eβ, xs_1β ++ xs_2β ++ ysβ) (n1β, some xs_1β)
aβ : Interpretation V_N V_T R (eβ.star, xs_2β ++ ysβ) (n2β, some xs_2β)
ih :
β m < n1β + n2β + 1,
β (e : PE V_N V_T),
Interpretation V_N V_T R (e, xs_1β ++ xs_2β ++ ysβ) (m, some (xs_1β ++ xs_2β)) β
(xs_1β ++ xs_2β).IsPrefix (xs_1β ++ xs_2β ++ ysβ)
β’ (xs_1β ++ xs_2β).IsPrefix (xs_1β ++ xs_2β ++ ysβ)
case star_termination
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some []) β [].IsPrefix xs
β’ [].IsPrefix xs
case notP_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some []) β [].IsPrefix xs
β’ [].IsPrefix xs | case nonTerminal
V_N V_T : Type
R : V_N β PE V_N V_T
xs ys : List V_T
Aβ : V_N
nβ : β
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some ys) β ys.IsPrefix xs
aβ : Interpretation V_N V_T R (R Aβ, xs) (nβ, some ys)
β’ ys.IsPrefix xs
case choice_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs ys : List V_T
e1β e2β : PE V_N V_T
n1β n2β : β
aβΒΉ : Interpretation V_N V_T R (e1β, xs) (n1β, none)
ih : β m < n1β + n2β + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some ys) β ys.IsPrefix xs
aβ : Interpretation V_N V_T R (e2β, xs) (n2β, some ys)
β’ ys.IsPrefix xs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationPrefix | [264, 1] | [285, 20] | first | apply EmptyStringPrefix | apply CharPrefix | apply PrefixAppend | case notP_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some []) β [].IsPrefix xs
β’ [].IsPrefix xs | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationPrefix | [264, 1] | [285, 20] | apply EmptyStringPrefix | case notP_2
V_N V_T : Type
R : V_N β PE V_N V_T
xs : List V_T
eβ : PE V_N V_T
nβ : β
aβ : Interpretation V_N V_T R (eβ, xs) (nβ, none)
ih : β m < nβ + 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, xs) (m, some []) β [].IsPrefix xs
β’ [].IsPrefix xs | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Program/PEG.lean | InterpretationPrefix | [264, 1] | [285, 20] | apply CharPrefix | case terminal_success
V_N V_T : Type
R : V_N β PE V_N V_T
aβ : V_T
xsβ : List V_T
ih : β m < 1, β (e : PE V_N V_T), Interpretation V_N V_T R (e, aβ :: xsβ) (m, some [aβ]) β [aβ].IsPrefix (aβ :: xsβ)
β’ [aβ].IsPrefix (aβ :: xsβ) | no goals |
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