apply (Model.PropFun.agreeOn_semVars _).mpr h2
case h.right
ν : Type u_1
s : LawfulState ν
n : ℕ
σ : PropAssignment IVar
h2 : σ ⊨ Cnf.toPropFun s.cnf
σ' : PropAssignment IVar
h1 :
  PropAssignment.map Sum.inl (PropAssignment.map (⇑{ toFun := State.withTemps.vMap s.toState, inj' := ⋯ }) σ') =
    PropAssignment.map s.vMap σ
⊢ PropAssignment.setMany σ (Finset.image (fun x => State.withTemps.vMap s.toState (Sum.inr x)) Finset.univ) σ' ⊨
    Cnf.toPropFun s.cnf
ν : Type u_1
s : LawfulState ν
n : ℕ
σ : PropAssignment IVar
h2 : σ ⊨ Cnf.toPropFun s.cnf
σ' : PropAssignment IVar
h1 :
  PropAssignment.map Sum.inl (PropAssignment.map (⇑{ toFun := State.withTemps.vMap s.toState, inj' := ⋯ }) σ') =
    PropAssignment.map s.vMap σ
⊢ PropAssignment.agreeOn (↑(PropFun.semVars (Cnf.toPropFun s.cnf)))
    (PropAssignment.setMany σ (Finset.image (fun x => State.withTemps.vMap s.toState (Sum.inr x)) Finset.univ) σ') σ