Theorem: BVExpr.bitblast.blastVar.go_decl_eq (LeanSAT/Reflect/BVExpr/BitBlast/Impl/Var.lean)

State before:
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < (go w aig i s a hi).aig.decls.size),
    (go w aig i s a hi).aig.decls[idx] = aig.decls[idx]
Tactic:
generalize hgo : go w aig i s a hi = res
State after:
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
hgo : go w aig i s a hi = res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

State before:
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
hgo : go w aig i s a hi = 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
State after:
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
hgo :
  (if hidx : i < w then
      let res := aig.mkAtomCached (BVBit.mk a ⟨i, hidx⟩);
      let aig_1 := res.aig;
      let bitRef := res.ref;
      let s := s.cast ⋯;
      let s := s.pushRef bitRef;
      go w aig_1 (i + 1) s a ⋯
    else
      let_fun hidx := ⋯;
      { aig := aig, stream := hidx ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

State before:
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
hgo :
  (if hidx : i < w then
      let res := aig.mkAtomCached (BVBit.mk a ⟨i, hidx⟩);
      let aig_1 := res.aig;
      let bitRef := res.ref;
      let s := s.cast ⋯;
      let s := s.pushRef bitRef;
      go w aig_1 (i + 1) s a ⋯
    else
      let_fun hidx := ⋯;
      { aig := aig, stream := hidx ▸ 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
State after:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  (let res := aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩);
    let aig_1 := res.aig;
    let bitRef := res.ref;
    let s := s.cast ⋯;
    let s := s.pushRef bitRef;
    go w aig_1 (i + 1) s a ⋯) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo :
  (let_fun hidx := ⋯;
    { aig := aig, stream := hidx ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

State before:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  (let res := aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩);
    let aig_1 := res.aig;
    let bitRef := res.ref;
    let s := s.cast ⋯;
    let s := s.pushRef bitRef;
    go w aig_1 (i + 1) s a ⋯) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo :
  (let_fun hidx := ⋯;
    { aig := aig, stream := hidx ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Tactic:
. dsimp at hgo
  rw [← hgo]
  intro idx h1 h2
  rw [blastVar.go_decl_eq]
  rw [AIG.LawfulOperator.decl_eq (f := AIG.mkAtomCached)]
  apply AIG.LawfulOperator.lt_size_of_lt_aig_size (f := AIG.mkAtomCached)
  assumption
State after:
case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo :
  (let_fun hidx := ⋯;
    { aig := aig, stream := hidx ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

State before:
case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo :
  (let_fun hidx := ⋯;
    { aig := aig, stream := hidx ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Tactic:
. dsimp at hgo
  rw [← hgo]
  intros
  simp
State after:
no goals

State before:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  (let res := aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩);
    let aig_1 := res.aig;
    let bitRef := res.ref;
    let s := s.cast ⋯;
    let s := s.pushRef bitRef;
    go w aig_1 (i + 1) s a ⋯) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Tactic:
dsimp at hgo
State after:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

State before:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Tactic:
rw [← hgo]
State after:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size)
    (h2 :
      idx <
        (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
                ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size),
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
              ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls[idx] =
      aig.decls[idx]

State before:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size)
    (h2 :
      idx <
        (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
                ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size),
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
              ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls[idx] =
      aig.decls[idx]
Tactic:
intro idx h1 h2
State after:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size
⊢ (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls[idx] =
    aig.decls[idx]

State before:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size
⊢ (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls[idx] =
    aig.decls[idx]
Tactic:
rw [blastVar.go_decl_eq]
State after:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size
⊢ (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig.decls[idx] = aig.decls[idx]

case isTrue.h1
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size
⊢ idx < (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig.decls.size

State before:
case isTrue
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size
⊢ (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig.decls[idx] = aig.decls[idx]

case isTrue.h1
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size
⊢ idx < (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig.decls.size
Tactic:
rw [AIG.LawfulOperator.decl_eq (f := AIG.mkAtomCached)]
State after:
case isTrue.h2
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size
⊢ idx < (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig.decls.size

State before:
case isTrue.h2
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size
⊢ idx < (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig.decls.size
Tactic:
apply AIG.LawfulOperator.lt_size_of_lt_aig_size (f := AIG.mkAtomCached)
State after:
case isTrue.h2.h
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size
⊢ idx < aig.decls.size

State before:
case isTrue.h2.h
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : i < w
hgo :
  go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
      ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯ =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go w (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).aig (i + 1)
            ((s.cast ⋯).pushRef (aig.mkAtomCached (BVBit.mk a ⟨i, h✝⟩)).ref) a ⋯).aig.decls.size
⊢ idx < aig.decls.size
Tactic:
assumption
State after:
no goals

State before:
case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo :
  (let_fun hidx := ⋯;
    { aig := aig, stream := hidx ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Tactic:
dsimp at hgo
State after:
case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo : { aig := aig, stream := ⋯ ▸ s } = res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

State before:
case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo : { aig := aig, stream := ⋯ ▸ s } = res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]
Tactic:
rw [← hgo]
State after:
case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo : { aig := aig, stream := ⋯ ▸ s } = res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < { aig := aig, stream := ⋯ ▸ s }.aig.decls.size),
    { aig := aig, stream := ⋯ ▸ s }.aig.decls[idx] = aig.decls[idx]

State before:
case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo : { aig := aig, stream := ⋯ ▸ s } = res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < { aig := aig, stream := ⋯ ▸ s }.aig.decls.size),
    { aig := aig, stream := ⋯ ▸ s }.aig.decls[idx] = aig.decls[idx]
Tactic:
intros
State after:
case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo : { aig := aig, stream := ⋯ ▸ s } = res
idx✝ : Nat
h1✝ : idx✝ < aig.decls.size
h2✝ : idx✝ < { aig := aig, stream := ⋯ ▸ s }.aig.decls.size
⊢ { aig := aig, stream := ⋯ ▸ s }.aig.decls[idx✝] = aig.decls[idx✝]

State before:
case isFalse
w : Nat
aig : AIG BVBit
i : Nat
s : aig.RefStream i
a : Nat
hi : i ≤ w
res : AIG.RefStreamEntry BVBit w
h✝ : ¬i < w
hgo : { aig := aig, stream := ⋯ ▸ s } = res
idx✝ : Nat
h1✝ : idx✝ < aig.decls.size
h2✝ : idx✝ < { aig := aig, stream := ⋯ ▸ s }.aig.decls.size
⊢ { aig := aig, stream := ⋯ ▸ s }.aig.decls[idx✝] = aig.decls[idx✝]
Tactic:
simp
State after:
no goals