Theorem: BVExpr.bitblast.blastAdd.go_getRef_aux
Proof state before:
case isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
cin : aig.Ref
s : aig.RefStream curr
lhs rhs : aig.RefStream w
idx : Nat
hidx : idx < curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
      ((s.cast ⋯).pushRef (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
      (lhs.cast ⋯) (rhs.cast ⋯) =
    res
hfoo :
  aig.decls.size ≤
    (go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
            ((s.cast ⋯).pushRef
              (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
            (lhs.cast ⋯) (rhs.cast ⋯)).aig.decls.size
⊢ ((s.getRef idx ?isTrue.hidx).cast ⋯).gate = (s.getRef idx hidx).gate

case isTrue.hidx
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
cin : aig.Ref
s : aig.RefStream curr
lhs rhs : aig.RefStream w
idx : Nat
hidx : idx < curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
      ((s.cast ⋯).pushRef (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
      (lhs.cast ⋯) (rhs.cast ⋯) =
    res
hfoo :
  aig.decls.size ≤
    (go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
            ((s.cast ⋯).pushRef
              (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
            (lhs.cast ⋯) (rhs.cast ⋯)).aig.decls.size
⊢ idx < curr
Tactic:
. simp
Proof state after:
case isTrue.hidx
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
cin : aig.Ref
s : aig.RefStream curr
lhs rhs : aig.RefStream w
idx : Nat
hidx : idx < curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
      (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
      ((s.cast ⋯).pushRef (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
      (lhs.cast ⋯) (rhs.cast ⋯) =
    res
hfoo :
  aig.decls.size ≤
    (go (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).aig (curr + 1) ⋯
            (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).cout
            ((s.cast ⋯).pushRef
              (mkFullAdder aig { lhs := lhs.getRef curr h✝, rhs := rhs.getRef curr h✝, cin := cin }).out)
            (lhs.cast ⋯) (rhs.cast ⋯)).aig.decls.size
⊢ idx < curr