simp only [isFreeIn] at h1_1
D : Type
I : Interpretation D
E : Env
v t : VarName
F F' : Formula
h1_x : VarName
h1_phi : Formula
h1_v h1_t : VarName
h1_1 : ¬isFreeIn h1_v (exists_ h1_x h1_phi)
V : VarAssignment D
⊢ Holds D I (Function.updateITE V h1_v (V h1_t)) E (exists_ h1_x h1_phi) ↔ Holds D I V E (exists_ h1_x h1_phi)
D : Type
I : Interpretation D
E : Env
v t : VarName
F F' : Formula
h1_x : VarName
h1_phi : Formula
h1_v h1_t : VarName
h1_1 : ¬(¬h1_v = h1_x ∧ isFreeIn h1_v h1_phi)
V : VarAssignment D
⊢ Holds D I (Function.updateITE V h1_v (V h1_t)) E (exists_ h1_x h1_phi) ↔ Holds D I V E (exists_ h1_x h1_phi)