Theorem: AIG.RefStream.ite.denote_go
Proof state before:
case isTrue.inl
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
assign : α → Bool
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
discr : aig.Ref
lhs rhs : aig.RefStream w
s : aig.RefStream curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig (curr + 1) ⋯
      { gate := discr.gate, hgate := ⋯ } (lhs.cast ⋯) (rhs.cast ⋯)
      ((s.cast ⋯).pushRef
        (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref) =
    res
hidx1 : curr < w
hidx2 : curr ≤ curr
⊢ ⟦{
        aig :=
          (go (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig (curr + 1) ⋯
              { gate := discr.gate, hgate := ⋯ } (lhs.cast ⋯) (rhs.cast ⋯)
              ((s.cast ⋯).pushRef
                (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref)).aig,
        ref := (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref.cast ⋯ },
      assign⟧ =
    if ⟦{ aig := aig, ref := discr }, assign⟧ = true then ⟦{ aig := aig, ref := lhs.getRef curr hidx1 }, assign⟧
    else ⟦{ aig := aig, ref := rhs.getRef curr hidx1 }, assign⟧
Tactic:
rw [go_denote_mem_prefix]
Proof state after:
case isTrue.inl
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
assign : α → Bool
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
discr : aig.Ref
lhs rhs : aig.RefStream w
s : aig.RefStream curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig (curr + 1) ⋯
      { gate := discr.gate, hgate := ⋯ } (lhs.cast ⋯) (rhs.cast ⋯)
      ((s.cast ⋯).pushRef
        (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref) =
    res
hidx1 : curr < w
hidx2 : curr ≤ curr
⊢ ⟦{ aig := (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig,
        ref :=
          {
            gate :=
              ((aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref.cast
                  ⋯).gate,
            hgate := ?isTrue.inl.hstart } },
      assign⟧ =
    if ⟦{ aig := aig, ref := discr }, assign⟧ = true then ⟦{ aig := aig, ref := lhs.getRef curr hidx1 }, assign⟧
    else ⟦{ aig := aig, ref := rhs.getRef curr hidx1 }, assign⟧

case isTrue.inl.hstart
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
assign : α → Bool
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
discr : aig.Ref
lhs rhs : aig.RefStream w
s : aig.RefStream curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig (curr + 1) ⋯
      { gate := discr.gate, hgate := ⋯ } (lhs.cast ⋯) (rhs.cast ⋯)
      ((s.cast ⋯).pushRef
        (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref) =
    res
hidx1 : curr < w
hidx2 : curr ≤ curr
⊢ ((aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref.cast ⋯).gate <
    (aig.mkIfCached { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig.decls.size