cases Nat.eq_or_lt_of_le hidx2 with
| inl heq => simpa [heq] using h2
| inr hlt =>
  specialize h3 idx hidx1 (by omega)
  rw [← h3]
  rw [AIG.LawfulOperator.denote_mem_prefix (f := AIG.mkAndCached)]
  . simp
  . simp [Ref.hgate]
case isTrue.mp.intro.intro.right
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig✝ : AIG α
len : Nat
assign : α → Bool
aig : AIG α
acc : aig.Ref
curr : Nat
hcurr : curr ≤ len
input : aig.RefStream len
res : Entrypoint α
h✝ : curr < len
hgo :
  go (aig.mkAndCached { lhs := acc, rhs := input.getRef curr h✝ }).aig
      (aig.mkAndCached { lhs := acc, rhs := input.getRef curr h✝ }).ref (curr + 1) len (input.cast ⋯) mkAndCached =
    res
h3 :
  ∀ (idx : Nat) (hidx1 : idx < len),
    curr + 1 ≤ idx →
      ⟦{ aig := (aig.mkAndCached { lhs := acc, rhs := input.getRef curr h✝ }).aig,
            ref := (input.getRef idx hidx1).cast ⋯ },
          assign⟧ =
        true
h1 : ⟦{ aig := aig, ref := acc }, assign⟧ = true
h2 : ⟦{ aig := aig, ref := input.getRef curr h✝ }, assign⟧ = true
idx : Nat
hidx1 : idx < len
hidx2 : curr ≤ idx
⊢ ⟦{ aig := aig, ref := input.getRef idx hidx1 }, assign⟧ = true
no goals