Theorem: AIG.RefStream.zip.denote_go
Proof state before:
case isTrue.inl
α : Type
inst✝³ : BEq α
inst✝² : Hashable α
inst✝¹ : DecidableEq α
aig✝ : AIG α
len : Nat
assign : α → Bool
aig : AIG α
curr : Nat
hcurr : curr ≤ len
s : aig.RefStream curr
lhs rhs : aig.RefStream len
f : (aig : AIG α) → aig.BinaryInput → Entrypoint α
inst✝ : LawfulOperator α BinaryInput f
chainable : LawfulZipOperator α f
idx : Nat
hidx1 : idx < len
hidx2 : curr ≤ idx
res : RefStreamEntry α len
h✝ : curr < len
hgo :
  go (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig (curr + 1)
      ((s.cast ⋯).pushRef (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref) ⋯ (lhs.cast ⋯)
      (rhs.cast ⋯) f =
    res
heq : curr = idx
⊢ ⟦{
        aig :=
          (go (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig (curr + 1)
              ((s.cast ⋯).pushRef (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref) ⋯ (lhs.cast ⋯)
              (rhs.cast ⋯) f).aig,
        ref :=
          (((s.cast ⋯).pushRef (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref).getRef idx
                ?isTrue.inl.hidx).cast
            ⋯ },
      assign⟧ =
    ⟦f aig { lhs := lhs.getRef idx hidx1, rhs := rhs.getRef idx hidx1 }, assign⟧

case isTrue.inl.hidx
α : Type
inst✝³ : BEq α
inst✝² : Hashable α
inst✝¹ : DecidableEq α
aig✝ : AIG α
len : Nat
assign : α → Bool
aig : AIG α
curr : Nat
hcurr : curr ≤ len
s : aig.RefStream curr
lhs rhs : aig.RefStream len
f : (aig : AIG α) → aig.BinaryInput → Entrypoint α
inst✝ : LawfulOperator α BinaryInput f
chainable : LawfulZipOperator α f
idx : Nat
hidx1 : idx < len
hidx2 : curr ≤ idx
res : RefStreamEntry α len
h✝ : curr < len
hgo :
  go (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig (curr + 1)
      ((s.cast ⋯).pushRef (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref) ⋯ (lhs.cast ⋯)
      (rhs.cast ⋯) f =
    res
heq : curr = idx
⊢ idx < curr + 1
Tactic:
rw [AIG.RefStream.getRef_push_ref_eq']
Proof state after:
case isTrue.inl
α : Type
inst✝³ : BEq α
inst✝² : Hashable α
inst✝¹ : DecidableEq α
aig✝ : AIG α
len : Nat
assign : α → Bool
aig : AIG α
curr : Nat
hcurr : curr ≤ len
s : aig.RefStream curr
lhs rhs : aig.RefStream len
f : (aig : AIG α) → aig.BinaryInput → Entrypoint α
inst✝ : LawfulOperator α BinaryInput f
chainable : LawfulZipOperator α f
idx : Nat
hidx1 : idx < len
hidx2 : curr ≤ idx
res : RefStreamEntry α len
h✝ : curr < len
hgo :
  go (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig (curr + 1)
      ((s.cast ⋯).pushRef (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref) ⋯ (lhs.cast ⋯)
      (rhs.cast ⋯) f =
    res
heq : curr = idx
⊢ ⟦{
        aig :=
          (go (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig (curr + 1)
              ((s.cast ⋯).pushRef (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref) ⋯ (lhs.cast ⋯)
              (rhs.cast ⋯) f).aig,
        ref := (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref.cast ⋯ },
      assign⟧ =
    ⟦f aig { lhs := lhs.getRef idx hidx1, rhs := rhs.getRef idx hidx1 }, assign⟧

case isTrue.inl.hidx
α : Type
inst✝³ : BEq α
inst✝² : Hashable α
inst✝¹ : DecidableEq α
aig✝ : AIG α
len : Nat
assign : α → Bool
aig : AIG α
curr : Nat
hcurr : curr ≤ len
s : aig.RefStream curr
lhs rhs : aig.RefStream len
f : (aig : AIG α) → aig.BinaryInput → Entrypoint α
inst✝ : LawfulOperator α BinaryInput f
chainable : LawfulZipOperator α f
idx : Nat
hidx1 : idx < len
hidx2 : curr ≤ idx
res : RefStreamEntry α len
h✝ : curr < len
hgo :
  go (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).aig (curr + 1)
      ((s.cast ⋯).pushRef (f aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝ }).ref) ⋯ (lhs.cast ⋯)
      (rhs.cast ⋯) f =
    res
heq : curr = idx
⊢ idx = curr