simp only [List.map_eq_map_iff]
case a.h.e'_4
D : Type
I : Interpretation D
E : Env
σ : VarName → VarName
binders : Finset VarName
F F' : Formula
σ' : VarName → VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : ∀ v ∈ xs', v ∉ binders' → σ' v ∉ binders'
V V' : VarAssignment D
h2 : ∀ v ∈ binders', V v = V' (σ' v)
h3 : ∀ (v : VarName), σ' v ∉ binders' → V v = V' (σ' v)
h4 : ∀ v ∈ binders', v = σ' v
⊢ List.map V xs' = List.map (V' ∘ σ') xs'
case a.h.e'_4
D : Type
I : Interpretation D
E : Env
σ : VarName → VarName
binders : Finset VarName
F F' : Formula
σ' : VarName → VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : ∀ v ∈ xs', v ∉ binders' → σ' v ∉ binders'
V V' : VarAssignment D
h2 : ∀ v ∈ binders', V v = V' (σ' v)
h3 : ∀ (v : VarName), σ' v ∉ binders' → V v = V' (σ' v)
h4 : ∀ v ∈ binders', v = σ' v
⊢ ∀ x ∈ xs', V x = (V' ∘ σ') x