Theorem: FOL.NV.Sub.Pred.One.Rec.substitution_theorem (FOL/NV/Sub/Pred/One/Rec/Sub.lean)

State before:
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
F : Formula
P : PredName
zs : List VarName
H : Formula
h1 : admits P zs H F
⊢ Holds D (I' D I V E P zs H) V E F ↔ Holds D I V E (replace P zs H F)
Tactic:
apply substitution_theorem_aux D I V V E F P zs H ∅
State after:
case h1
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
F : Formula
P : PredName
zs : List VarName
H : Formula
h1 : admits P zs H F
⊢ admitsAux P zs H ∅ F

case h2
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
F : Formula
P : PredName
zs : List VarName
H : Formula
h1 : admits P zs H F
⊢ ∀ x ∉ ∅, V x = V x

State before:
case h1
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
F : Formula
P : PredName
zs : List VarName
H : Formula
h1 : admits P zs H F
⊢ admitsAux P zs H ∅ F
Tactic:
exact h1
State after:
no goals

State before:
case h2
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
F : Formula
P : PredName
zs : List VarName
H : Formula
h1 : admits P zs H F
⊢ ∀ x ∉ ∅, V x = V x
Tactic:
simp
State after:
no goals