internlm/Lean-Github huggingface dataset:
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : curr < w
hgo : go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝)) = res
⊢ ∀ (hfoo : aig.decls.size ≤ res.aig.decls.size), res.stream.getRef idx ⋯ = (s.getRef idx hidx).cast hfoo
Tactic:
rw [← hgo]
Proof state after:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : curr < w
hgo : go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝)) = res
⊢ ∀ (hfoo : aig.decls.size ≤ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).aig.decls.size),
    (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).stream.getRef idx ⋯ =
      (s.getRef idx hidx).cast hfoo
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : curr < w
hgo : go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝)) = res
⊢ ∀ (hfoo : aig.decls.size ≤ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).aig.decls.size),
    (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).stream.getRef idx ⋯ =
      (s.getRef idx hidx).cast hfoo
Tactic:
intros
Proof state after:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : curr < w
hgo : go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝)) = res
hfoo✝ : aig.decls.size ≤ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).aig.decls.size
⊢ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).stream.getRef idx ⋯ =
    (s.getRef idx hidx).cast hfoo✝
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : curr < w
hgo : go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝)) = res
hfoo✝ : aig.decls.size ≤ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).aig.decls.size
⊢ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).stream.getRef idx ⋯ =
    (s.getRef idx hidx).cast hfoo✝
Tactic:
rw [go_getRef_aux]
Proof state after:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : curr < w
hgo : go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝)) = res
hfoo✝ : aig.decls.size ≤ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).aig.decls.size
⊢ ((s.pushRef (input.getRef curr h✝)).getRef idx ?isTrue.isTrue.hidx).cast ?isTrue.isTrue.hfoo =
    (s.getRef idx hidx).cast hfoo✝

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

case isTrue.isTrue.hfoo
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : curr < w
hgo : go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝)) = res
hfoo✝ : aig.decls.size ≤ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).aig.decls.size
⊢ aig.decls.size ≤ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).aig.decls.size
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : curr < w
hgo : go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝)) = res
hfoo✝ : aig.decls.size ≤ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).aig.decls.size
⊢ ((s.pushRef (input.getRef curr h✝)).getRef idx ?isTrue.isTrue.hidx).cast ?isTrue.isTrue.hfoo =
    (s.getRef idx hidx).cast hfoo✝

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

case isTrue.isTrue.hfoo
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : curr < w
hgo : go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝)) = res
hfoo✝ : aig.decls.size ≤ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).aig.decls.size
⊢ aig.decls.size ≤ (go aig w input newWidth (curr + 1) ⋯ (s.pushRef (input.getRef curr h✝))).aig.decls.size
Tactic:
rw [AIG.RefStream.getRef_push_ref_lt]
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
⊢ ∀ (hfoo : aig.decls.size ≤ res.aig.decls.size), res.stream.getRef idx ⋯ = (s.getRef idx hidx).cast hfoo
Tactic:
rw [← hgo]
Proof state after:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
⊢ ∀
    (hfoo :
      aig.decls.size ≤
        (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
                ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size),
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
              ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).stream.getRef
        idx ⋯ =
      (s.getRef idx hidx).cast hfoo
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
⊢ ∀
    (hfoo :
      aig.decls.size ≤
        (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
                ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size),
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
              ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).stream.getRef
        idx ⋯ =
      (s.getRef idx hidx).cast hfoo
Tactic:
intros
Proof state after:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).stream.getRef
      idx ⋯ =
    (s.getRef idx hidx).cast hfoo✝
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).stream.getRef
      idx ⋯ =
    (s.getRef idx hidx).cast hfoo✝
Tactic:
rw [go_getRef_aux]
Proof state after:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ (((s.cast ⋯).pushRef (aig.mkConstCached false).ref).getRef idx ?isTrue.isFalse.hidx).cast ?isTrue.isFalse.hfoo =
    (s.getRef idx hidx).cast hfoo✝

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

case isTrue.isFalse.hfoo
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ (aig.mkConstCached false).aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse.hfoo
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ (aig.mkConstCached false).aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size

case isTrue.isFalse.hfoo
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ (aig.mkConstCached false).aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
Tactic:
. apply go_le_size
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ ((s.cast ⋯).getRef idx ?isTrue.isFalse.hidx).cast ?isTrue.isFalse.hfoo = (s.getRef idx hidx).cast hfoo✝
Tactic:
simp only [Ref.cast, Ref.mk.injEq]
Proof state after:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ ((s.cast ⋯).getRef idx ?isTrue.isFalse.hidx).gate = (s.getRef idx hidx).gate
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ ((s.cast ⋯).getRef idx ?isTrue.isFalse.hidx).gate = (s.getRef idx hidx).gate
Tactic:
rw [AIG.RefStream.getRef_cast]
Proof state after:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ ((s.getRef idx ?isTrue.isFalse.hidx).cast ⋯).gate = (s.getRef idx hidx).gate

case isTrue.isFalse.hidx
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ idx < curr
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ ((s.getRef idx ?isTrue.isFalse.hidx).cast ⋯).gate = (s.getRef idx hidx).gate

case isTrue.isFalse.hidx
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ idx < curr
Tactic:
. simp
Proof state after:
case isTrue.isFalse.hidx
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ idx < curr
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse.hidx
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ idx < curr
Tactic:
. assumption
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ ((s.getRef idx ?isTrue.isFalse.hidx).cast ⋯).gate = (s.getRef idx hidx).gate
Tactic:
simp
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse.hidx
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ idx < curr
Tactic:
assumption
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastZeroExtend.go_getRef_aux
Proof state before:
case isTrue.isFalse.hfoo
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
aig : AIG α
w : Nat
input : aig.RefStream w
newWidth curr : Nat
hcurr : curr ≤ newWidth
s : aig.RefStream curr
idx : Nat
hidx : idx < curr
res : RefStreamEntry α newWidth
h✝¹ : curr < newWidth
h✝ : ¬curr < w
hgo :
  go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
      ((s.cast ⋯).pushRef (aig.mkConstCached false).ref) =
    res
hfoo✝ :
  aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ (aig.mkConstCached false).aig.decls.size ≤
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
Tactic:
apply go_le_size
Proof state after:
no goals