rw [AIG.LawfulOperator.decl_eq (f := mkFullAdderCarry)]
case isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
curr a✝ : Nat
hcurr : curr ≤ a✝
aig : AIG α
cin : aig.Ref
lhs rhs : aig.RefStream a✝
res : AIG.Entrypoint α
h✝ : curr < a✝
hgo :
  go (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).ref (lhs.cast ⋯)
      (rhs.cast ⋯) =
    res
idx✝ : Nat
h1✝ : idx✝ < aig.decls.size
h2✝ :
  idx✝ <
    (go (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).ref (lhs.cast ⋯)
            (rhs.cast ⋯)).aig.decls.size
⊢ (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig.decls[idx✝] =
    aig.decls[idx✝]

case isTrue.h1
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
curr a✝ : Nat
hcurr : curr ≤ a✝
aig : AIG α
cin : aig.Ref
lhs rhs : aig.RefStream a✝
res : AIG.Entrypoint α
h✝ : curr < a✝
hgo :
  go (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).ref (lhs.cast ⋯)
      (rhs.cast ⋯) =
    res
idx✝ : Nat
h1✝ : idx✝ < aig.decls.size
h2✝ :
  idx✝ <
    (go (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).ref (lhs.cast ⋯)
            (rhs.cast ⋯)).aig.decls.size
⊢ idx✝ < (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig.decls.size
case isTrue.h2
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
curr a✝ : Nat
hcurr : curr ≤ a✝
aig : AIG α
cin : aig.Ref
lhs rhs : aig.RefStream a✝
res : AIG.Entrypoint α
h✝ : curr < a✝
hgo :
  go (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).ref (lhs.cast ⋯)
      (rhs.cast ⋯) =
    res
idx✝ : Nat
h1✝ : idx✝ < aig.decls.size
h2✝ :
  idx✝ <
    (go (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).ref (lhs.cast ⋯)
            (rhs.cast ⋯)).aig.decls.size
⊢ idx✝ < (mkFullAdderCarry aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig.decls.size