case _ c1 =>
  simp only [c1] at phi_ih
  simp at phi_ih
  exact phi_ih h1
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
  ↑phi.primeSet ⊆ Δ_U →
    IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
c1 : ¬evalPrime V phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_
no goals