-- Mathlib/.lake/packages/lean4/src/lean/Std/Tactic/BVDecide/Bitblast/BVExpr/Circuit/Impl/Operations/Udiv.lean
theorem go_decl_eq (aig : AIG α) (curr : Nat) (falseRef trueRef : AIG.Ref aig)
     (n d : AIG.RefVec aig w) (wn wr : Nat) (q r : AIG.RefVec aig w) :
    ∀ (idx : Nat) (h1) (h2),
        (go aig curr falseRef trueRef n d wn wr q r).aig.decls[idx]'h2 = aig.decls[idx]'h1

Proof state:
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
falseRef trueRef : aig.Ref
n d : aig.RefVec w
wn wr : Nat
q r : aig.RefVec w
res : BlastUdivOutput aig w
hgo :
  (match curr with
    | 0 => { aig := aig, q := q, r := r, hle := ⋯ }
    | curr.succ =>
      {
        aig :=
          (go (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).aig curr (falseRef.cast ⋯) (trueRef.cast ⋯)
              (n.cast ⋯) (d.cast ⋯) (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wn
              (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wr
              (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).q
              (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).r).aig,
        q :=
          (go (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).aig curr (falseRef.cast ⋯) (trueRef.cast ⋯)
              (n.cast ⋯) (d.cast ⋯) (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wn
              (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wr
              (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).q
              (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).r).q,
        r :=
          (go (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).aig curr (falseRef.cast ⋯) (trueRef.cast ⋯)
              (n.cast ⋯) (d.cast ⋯) (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wn
              (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wr
              (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).q
              (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).r).r,
        hle := ⋯ }) =
    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

Result:
case h_1
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
falseRef trueRef : aig.Ref
n d : aig.RefVec w
wn wr : Nat
q r : aig.RefVec w
res : BlastUdivOutput aig w
curr✝ : Nat
hgo : { aig := aig, q := q, r := r, hle := ⋯ } = res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

case h_2
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
falseRef trueRef : aig.Ref
n d : aig.RefVec w
wn wr : Nat
q r : aig.RefVec w
res : BlastUdivOutput aig w
curr✝¹ curr✝ : Nat
hgo :
  {
      aig :=
        (go (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).aig curr✝ (falseRef.cast ⋯) (trueRef.cast ⋯)
            (n.cast ⋯) (d.cast ⋯) (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wn
            (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wr
            (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).q
            (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).r).aig,
      q :=
        (go (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).aig curr✝ (falseRef.cast ⋯) (trueRef.cast ⋯)
            (n.cast ⋯) (d.cast ⋯) (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wn
            (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wr
            (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).q
            (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).r).q,
      r :=
        (go (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).aig curr✝ (falseRef.cast ⋯) (trueRef.cast ⋯)
            (n.cast ⋯) (d.cast ⋯) (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wn
            (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).wr
            (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).q
            (blastDivSubtractShift aig falseRef trueRef n d wn wr q r).r).r,
      hle := ⋯ } =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

Proof state:
case h_1
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
falseRef trueRef : aig.Ref
n d : aig.RefVec w
wn wr : Nat
q r : aig.RefVec w
res : BlastUdivOutput aig w
curr✝ : Nat
hgo : { aig := aig, q := q, r := r, hle := ⋯ } = res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

Tactic:
simp [← hgo]

Result:
no goals