internlm/Lean-Github huggingface dataset:
Theorem: BVExpr.bitblast.blastZeroExtend.go_decl_eq
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
res : AIG.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
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (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[idx] = aig.decls[idx]

case isTrue.isFalse.h1
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
res : AIG.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
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ idx < (aig.mkConstCached false).aig.decls.size
Tactic:
rw [AIG.LawfulOperator.decl_eq (f := AIG.mkConstCached)]
Proof state after:
case isTrue.isFalse.h2
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
res : AIG.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
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ idx < (aig.mkConstCached false).aig.decls.size
Theorem: BVExpr.bitblast.blastZeroExtend.go_decl_eq
Proof state before:
case isTrue.isFalse.h2
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
res : AIG.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
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ idx < (aig.mkConstCached false).aig.decls.size
Tactic:
apply AIG.LawfulOperator.lt_size_of_lt_aig_size (f := AIG.mkConstCached)
Proof state after:
case isTrue.isFalse.h2.h
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
res : AIG.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
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ idx < aig.decls.size
Theorem: BVExpr.bitblast.blastZeroExtend.go_decl_eq
Proof state before:
case isTrue.isFalse.h2.h
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
res : AIG.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
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go (aig.mkConstCached false).aig w (input.cast ⋯) newWidth (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
⊢ idx < aig.decls.size
Tactic:
assumption
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastZeroExtend.go_decl_eq
Proof state before:
case 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
res : AIG.RefStreamEntry α newWidth
h✝ : ¬curr < newWidth
hgo :
  (let_fun hcurr := ⋯;
    { aig := aig, stream := hcurr ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Tactic:
simp [← hgo]
Proof state after:
no goals
Theorem: bitvec_AndOrXor_1230__A__B___A__B
Proof state before:
⊢ ∀ (notOp0 notOp1 : BitVec 64), (notOp0 ^^^ -1) &&& (notOp1 ^^^ -1) = (notOp0 ||| notOp1) ^^^ -1
Tactic:
intros
Proof state after:
notOp0✝ notOp1✝ : BitVec 64
⊢ (notOp0✝ ^^^ -1) &&& (notOp1✝ ^^^ -1) = (notOp0✝ ||| notOp1✝) ^^^ -1
Theorem: bitvec_AndOrXor_1230__A__B___A__B
Proof state before:
notOp0✝ notOp1✝ : BitVec 64
⊢ (notOp0✝ ^^^ -1) &&& (notOp1✝ ^^^ -1) = (notOp0✝ ||| notOp1✝) ^^^ -1
Tactic:
bv_decide
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
⊢ aig.decls.size ≤ (go aig input distance curr hcurr s).aig.decls.size
Tactic:
unfold go
Proof state after:
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
⊢ aig.decls.size ≤
    (if hidx : curr < w then
            if hdist : distance + curr < w then
              let s := s.pushRef (input.getRef (distance + curr) ⋯);
              go aig input distance (curr + 1) ⋯ s
            else
              let res := aig.mkConstCached false;
              let aig_1 := res.aig;
              let zeroRef := res.ref;
              let_fun hfinal := ⋯;
              let s := s.cast hfinal;
              let input := input.cast hfinal;
              let s := s.pushRef zeroRef;
              go aig_1 input distance (curr + 1) ⋯ s
          else
            let_fun hcurr := ⋯;
            { aig := aig, stream := hcurr ▸ s }).aig.decls.size
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
⊢ aig.decls.size ≤
    (if hidx : curr < w then
            if hdist : distance + curr < w then
              let s := s.pushRef (input.getRef (distance + curr) ⋯);
              go aig input distance (curr + 1) ⋯ s
            else
              let res := aig.mkConstCached false;
              let aig_1 := res.aig;
              let zeroRef := res.ref;
              let_fun hfinal := ⋯;
              let s := s.cast hfinal;
              let input := input.cast hfinal;
              let s := s.pushRef zeroRef;
              go aig_1 input distance (curr + 1) ⋯ s
          else
            let_fun hcurr := ⋯;
            { aig := aig, stream := hcurr ▸ s }).aig.decls.size
Tactic:
split
Proof state after:
case isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝ : curr < w
⊢ aig.decls.size ≤
    (if hdist : distance + curr < w then
            let s := s.pushRef (input.getRef (distance + curr) ⋯);
            go aig input distance (curr + 1) ⋯ s
          else
            let res := aig.mkConstCached false;
            let aig_1 := res.aig;
            let zeroRef := res.ref;
            let_fun hfinal := ⋯;
            let s := s.cast hfinal;
            let input := input.cast hfinal;
            let s := s.pushRef zeroRef;
            go aig_1 input distance (curr + 1) ⋯ s).aig.decls.size

case isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝ : ¬curr < w
⊢ aig.decls.size ≤
    (let_fun hcurr := ⋯;
          { aig := aig, stream := hcurr ▸ s }).aig.decls.size
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
case isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝ : curr < w
⊢ aig.decls.size ≤
    (if hdist : distance + curr < w then
            let s := s.pushRef (input.getRef (distance + curr) ⋯);
            go aig input distance (curr + 1) ⋯ s
          else
            let res := aig.mkConstCached false;
            let aig_1 := res.aig;
            let zeroRef := res.ref;
            let_fun hfinal := ⋯;
            let s := s.cast hfinal;
            let input := input.cast hfinal;
            let s := s.pushRef zeroRef;
            go aig_1 input distance (curr + 1) ⋯ s).aig.decls.size

case isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝ : ¬curr < w
⊢ aig.decls.size ≤
    (let_fun hcurr := ⋯;
          { aig := aig, stream := hcurr ▸ s }).aig.decls.size
Tactic:
. dsimp
  split
  . refine Nat.le_trans ?_ (by apply go_le_size)
    omega
  . refine Nat.le_trans ?_ (by apply go_le_size)
    apply AIG.LawfulOperator.le_size
Proof state after:
case isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝ : ¬curr < w
⊢ aig.decls.size ≤
    (let_fun hcurr := ⋯;
          { aig := aig, stream := hcurr ▸ s }).aig.decls.size
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
case isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝ : ¬curr < w
⊢ aig.decls.size ≤
    (let_fun hcurr := ⋯;
          { aig := aig, stream := hcurr ▸ s }).aig.decls.size
Tactic:
. simp
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
case isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝ : curr < w
⊢ aig.decls.size ≤
    (if hdist : distance + curr < w then
            let s := s.pushRef (input.getRef (distance + curr) ⋯);
            go aig input distance (curr + 1) ⋯ s
          else
            let res := aig.mkConstCached false;
            let aig_1 := res.aig;
            let zeroRef := res.ref;
            let_fun hfinal := ⋯;
            let s := s.cast hfinal;
            let input := input.cast hfinal;
            let s := s.pushRef zeroRef;
            go aig_1 input distance (curr + 1) ⋯ s).aig.decls.size
Tactic:
dsimp
Proof state after:
case isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝ : curr < w
⊢ aig.decls.size ≤
    (if hdist : distance + curr < w then
            go aig input distance (curr + 1) ⋯ (s.pushRef (input.getRef (distance + curr) ⋯))
          else
            go (aig.mkConstCached false).aig (input.cast ⋯) distance (curr + 1) ⋯
              ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
case isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝ : curr < w
⊢ aig.decls.size ≤
    (if hdist : distance + curr < w then
            go aig input distance (curr + 1) ⋯ (s.pushRef (input.getRef (distance + curr) ⋯))
          else
            go (aig.mkConstCached false).aig (input.cast ⋯) distance (curr + 1) ⋯
              ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
Tactic:
split
Proof state after:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : distance + curr < w
⊢ aig.decls.size ≤ (go aig input distance (curr + 1) ⋯ (s.pushRef (input.getRef (distance + curr) ⋯))).aig.decls.size

case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : ¬distance + curr < w
⊢ aig.decls.size ≤
    (go (aig.mkConstCached false).aig (input.cast ⋯) distance (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : distance + curr < w
⊢ aig.decls.size ≤ (go aig input distance (curr + 1) ⋯ (s.pushRef (input.getRef (distance + curr) ⋯))).aig.decls.size

case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : ¬distance + curr < w
⊢ aig.decls.size ≤
    (go (aig.mkConstCached false).aig (input.cast ⋯) distance (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
Tactic:
. refine Nat.le_trans ?_ (by apply go_le_size)
  omega
Proof state after:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : ¬distance + curr < w
⊢ aig.decls.size ≤
    (go (aig.mkConstCached false).aig (input.cast ⋯) distance (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : ¬distance + curr < w
⊢ aig.decls.size ≤
    (go (aig.mkConstCached false).aig (input.cast ⋯) distance (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
Tactic:
. refine Nat.le_trans ?_ (by apply go_le_size)
  apply AIG.LawfulOperator.le_size
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : distance + curr < w
⊢ aig.decls.size ≤ (go aig input distance (curr + 1) ⋯ (s.pushRef (input.getRef (distance + curr) ⋯))).aig.decls.size
Tactic:
refine Nat.le_trans ?_ (by apply go_le_size)
Proof state after:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : distance + curr < w
⊢ aig.decls.size ≤ aig.decls.size
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
case isTrue.isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : distance + curr < w
⊢ aig.decls.size ≤ aig.decls.size
Tactic:
omega
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : distance + curr < w
⊢ ?m.16731 ≤ (go aig input distance (curr + 1) ⋯ (s.pushRef (input.getRef (distance + curr) ⋯))).aig.decls.size
Tactic:
apply go_le_size
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : ¬distance + curr < w
⊢ aig.decls.size ≤
    (go (aig.mkConstCached false).aig (input.cast ⋯) distance (curr + 1) ⋯
            ((s.cast ⋯).pushRef (aig.mkConstCached false).ref)).aig.decls.size
Tactic:
refine Nat.le_trans ?_ (by apply go_le_size)
Proof state after:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : ¬distance + curr < w
⊢ aig.decls.size ≤ (aig.mkConstCached false).aig.decls.size
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
case isTrue.isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : ¬distance + curr < w
⊢ aig.decls.size ≤ (aig.mkConstCached false).aig.decls.size
Tactic:
apply AIG.LawfulOperator.le_size
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastShiftRightConst.go_le_size
Proof state before:
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝¹ : curr < w
h✝ : ¬distance + curr < w
⊢ ?m.16859 ≤
    (go (aig.mkConstCached false).aig (input.cast ⋯) distance (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.blastShiftRightConst.go_le_size
Proof state before:
case isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
h✝ : ¬curr < w
⊢ aig.decls.size ≤
    (let_fun hcurr := ⋯;
          { aig := aig, stream := hcurr ▸ s }).aig.decls.size
Tactic:
simp
Proof state after:
no goals
Theorem: BVExpr.bitblast.blastShiftRightConst.go_decl_eq
Proof state before:
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < (go aig input distance curr hcurr s).aig.decls.size),
    (go aig input distance curr hcurr s).aig.decls[idx] = aig.decls[idx]
Tactic:
generalize hgo : go aig input distance curr hcurr s = res
Proof state after:
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
res : AIG.RefStreamEntry α w
hgo : go aig input distance curr hcurr s = res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Theorem: BVExpr.bitblast.blastShiftRightConst.go_decl_eq
Proof state before:
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
res : AIG.RefStreamEntry α w
hgo : go aig input distance curr hcurr s = res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Tactic:
unfold go at hgo
Proof state after:
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
res : AIG.RefStreamEntry α w
hgo :
  (if hidx : curr < w then
      if hdist : distance + curr < w then
        let s := s.pushRef (input.getRef (distance + curr) ⋯);
        go aig input distance (curr + 1) ⋯ s
      else
        let res := aig.mkConstCached false;
        let aig_1 := res.aig;
        let zeroRef := res.ref;
        let_fun hfinal := ⋯;
        let s := s.cast hfinal;
        let input := input.cast hfinal;
        let s := s.pushRef zeroRef;
        go aig_1 input distance (curr + 1) ⋯ s
    else
      let_fun hcurr := ⋯;
      { aig := aig, stream := hcurr ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Theorem: BVExpr.bitblast.blastShiftRightConst.go_decl_eq
Proof state before:
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
res : AIG.RefStreamEntry α w
hgo :
  (if hidx : curr < w then
      if hdist : distance + curr < w then
        let s := s.pushRef (input.getRef (distance + curr) ⋯);
        go aig input distance (curr + 1) ⋯ s
      else
        let res := aig.mkConstCached false;
        let aig_1 := res.aig;
        let zeroRef := res.ref;
        let_fun hfinal := ⋯;
        let s := s.cast hfinal;
        let input := input.cast hfinal;
        let s := s.pushRef zeroRef;
        go aig_1 input distance (curr + 1) ⋯ s
    else
      let_fun hcurr := ⋯;
      { aig := aig, stream := hcurr ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Tactic:
split at hgo
Proof state after:
case isTrue
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
res : AIG.RefStreamEntry α w
h✝ : curr < w
hgo :
  (if hdist : distance + curr < w then
      let s := s.pushRef (input.getRef (distance + curr) ⋯);
      go aig input distance (curr + 1) ⋯ s
    else
      let res := aig.mkConstCached false;
      let aig_1 := res.aig;
      let zeroRef := res.ref;
      let_fun hfinal := ⋯;
      let s := s.cast hfinal;
      let input := input.cast hfinal;
      let s := s.pushRef zeroRef;
      go aig_1 input distance (curr + 1) ⋯ s) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

case isFalse
α : Type
inst✝² : BEq α
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
distance : Nat
input : aig.RefStream w
curr : Nat
hcurr : curr ≤ w
s : aig.RefStream curr
res : AIG.RefStreamEntry α w
h✝ : ¬curr < w
hgo :
  (let_fun hcurr := ⋯;
    { aig := aig, stream := hcurr ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]