. apply LawfulOperator.lt_size_of_lt_aig_size
  apply LawfulOperator.lt_size_of_lt_aig_size
  assumption
case h2
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
idx : Nat
aig : AIG α
input : aig.BinaryInput
h : idx < aig.decls.size
h2 : idx < (aig.mkBEqCached input).aig.decls.size
⊢ idx <
    ((aig.mkGateCached (input.asGateInput false true)).aig.mkGateCached
            ((input.asGateInput true false).cast ⋯)).aig.decls.size
no goals