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 :=
          (((s.cast ⋯).pushRef
                    (aig.mkIfCached
                        { discr := discr, lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref).getRef
                curr ?isTrue.inl.hidx).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⟧

case isTrue.inl.hidx
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
⊢ curr < curr + 1
Tactic:
rw [AIG.RefStream.getRef_push_ref_eq']
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 :=
          (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⟧

case isTrue.inl.hidx
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
⊢ curr = curr