rw [AIG.RefStream.getRef_push_ref_lt]
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
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✝

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

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