rw [LawfulOperator.denote_mem_prefix (f := mkXorCached)]
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
assign : α → Bool
aig : AIG α
input : FullAdderInput aig
⊢ ⟦{ aig := (aig.mkXorCached { lhs := input.lhs, rhs := input.rhs }).aig,
        ref := { gate := input.cin.gate, hgate := ⋯ } },
      assign⟧ =
    ⟦{ aig := aig, ref := input.cin }, assign⟧
no goals