Theorem: BVExpr.bitblast.blastConst.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
c : BitVec w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref) c
      ⋯ =
    res
hfoo :
  aig.decls.size ≤
    (go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref)
            c ⋯).aig.decls.size
⊢ ((s.cast ⋯).getRef idx ?isTrue.hidx).cast ?isTrue.hfoo = (s.getRef idx hidx).cast hfoo

case isTrue.hidx
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
c : BitVec w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref) c
      ⋯ =
    res
hfoo :
  aig.decls.size ≤
    (go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref)
            c ⋯).aig.decls.size
⊢ idx < curr

case isTrue.hfoo
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
c : BitVec w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref) c
      ⋯ =
    res
hfoo :
  aig.decls.size ≤
    (go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref)
            c ⋯).aig.decls.size
⊢ (aig.mkConstCached (c.getLsb curr)).aig.decls.size ≤
    (go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref)
            c ⋯).aig.decls.size

case isTrue.hfoo
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
c : BitVec w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref) c
      ⋯ =
    res
hfoo :
  aig.decls.size ≤
    (go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref)
            c ⋯).aig.decls.size
⊢ (aig.mkConstCached (c.getLsb curr)).aig.decls.size ≤
    (go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref)
            c ⋯).aig.decls.size
Tactic:
. simp only [Ref.cast, Ref.mk.injEq]
  rw [AIG.RefStream.getRef_cast]
  . simp
  . assumption
Proof state after:
case isTrue.hfoo
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
c : BitVec w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref) c
      ⋯ =
    res
hfoo :
  aig.decls.size ≤
    (go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref)
            c ⋯).aig.decls.size
⊢ (aig.mkConstCached (c.getLsb curr)).aig.decls.size ≤
    (go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref)
            c ⋯).aig.decls.size

case isTrue.hfoo
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
c : BitVec w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α w
h✝ : curr < w
hgo :
  go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref) c
      ⋯ =
    res
hfoo :
  aig.decls.size ≤
    (go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref)
            c ⋯).aig.decls.size
⊢ (aig.mkConstCached (c.getLsb curr)).aig.decls.size ≤
    (go (aig.mkConstCached (c.getLsb curr)).aig (curr + 1) ((s.cast ⋯).pushRef (aig.mkConstCached (c.getLsb curr)).ref)
            c ⋯).aig.decls.size