simp
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ (if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ ∃ x ∈ Δ_U, (if evalPrime V x then x else x.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_