simp [this]
case h.left.h.inl
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
v : ν
this : σ' (State.withTemps.vMap s.toState (Sum.inl v)) = σ (s.vMap v)
⊢ (σ' ∘ State.withTemps.vMap s.toState) (Sum.inl v) =
    (PropAssignment.setMany σ (Finset.image (fun x => State.withTemps.vMap s.toState (Sum.inr x)) Finset.univ) σ' ∘
        State.withTemps.vMap s.toState)
      (Sum.inl v)
case h.left.h.inl
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
v : ν
this : σ' (State.withTemps.vMap s.toState (Sum.inl v)) = σ (s.vMap v)
⊢ σ (s.vMap v) =
    PropAssignment.setMany σ (Finset.image (fun x => State.withTemps.vMap s.toState (Sum.inr x)) Finset.univ) σ'
      (State.withTemps.vMap s.toState (Sum.inl v))