-- Mathlib/.lake/packages/lean4/src/lean/Std/Tactic/BVDecide/Bitblast/BVExpr/Circuit/Lemmas/Operations/Mul.lean
theorem go_denote_eq {w : Nat} (aig : AIG BVBit) (curr : Nat) (hcurr : curr + 1 ≤ w)
    (acc : AIG.RefVec aig w) (lhs rhs : AIG.RefVec aig w) (lexpr rexpr : BitVec w) (assign : Assignment)
    (hleft : ∀ (idx : Nat) (hidx : idx < w), ⟦aig, lhs.get idx hidx, assign.toAIGAssignment⟧ = lexpr.getLsbD idx)
    (hright : ∀ (idx : Nat) (hidx : idx < w), ⟦aig, rhs.get idx hidx, assign.toAIGAssignment⟧ = rexpr.getLsbD idx)
    (hacc : ∀ (idx : Nat) (hidx : idx < w),
                ⟦aig, acc.get idx hidx, assign.toAIGAssignment⟧
                  =
                (BitVec.mulRec lexpr rexpr curr).getLsbD idx) :
    ∀ (idx : Nat) (hidx : idx < w),
        ⟦
          (go aig lhs rhs (curr + 1) acc).aig,
          (go aig lhs rhs (curr + 1) acc).vec.get idx hidx,
          assign.toAIGAssignment
        ⟧
          =
        (BitVec.mulRec lexpr rexpr w).getLsbD idx

Proof state:
case hacc
w : Nat
aig : AIG BVBit
curr : Nat
hcurr : curr + 1 ≤ w
acc lhs rhs : aig.RefVec w
lexpr rexpr : BitVec w
assign : Assignment
hleft :
  ∀ (idx : Nat) (hidx : idx < w), ⟦assign.toAIGAssignment, { aig := aig, ref := lhs.get idx hidx }⟧ = lexpr.getLsbD idx
hright :
  ∀ (idx : Nat) (hidx : idx < w), ⟦assign.toAIGAssignment, { aig := aig, ref := rhs.get idx hidx }⟧ = rexpr.getLsbD idx
hacc :
  ∀ (idx : Nat) (hidx : idx < w),
    ⟦assign.toAIGAssignment, { aig := aig, ref := acc.get idx hidx }⟧ = (lexpr.mulRec rexpr curr).getLsbD idx
idx : Nat
hidx : idx < w
res : RefVecEntry BVBit w
h✝ : curr + 1 < w
hconstant : aig.isConstant (rhs.get (curr + 1) h✝) false = true
hgo : go aig lhs rhs (curr + 1 + 1) acc = res
⊢ ∀ (idx : Nat) (hidx : idx < w),
    ⟦assign.toAIGAssignment, { aig := aig, ref := acc.get idx hidx }⟧ = (lexpr.mulRec rexpr (curr + 1)).getLsbD idx

Tactic:
intro idx hidx

Result:
case hacc
w : Nat
aig : AIG BVBit
curr : Nat
hcurr : curr + 1 ≤ w
acc lhs rhs : aig.RefVec w
lexpr rexpr : BitVec w
assign : Assignment
hleft :
  ∀ (idx : Nat) (hidx : idx < w), ⟦assign.toAIGAssignment, { aig := aig, ref := lhs.get idx hidx }⟧ = lexpr.getLsbD idx
hright :
  ∀ (idx : Nat) (hidx : idx < w), ⟦assign.toAIGAssignment, { aig := aig, ref := rhs.get idx hidx }⟧ = rexpr.getLsbD idx
hacc :
  ∀ (idx : Nat) (hidx : idx < w),
    ⟦assign.toAIGAssignment, { aig := aig, ref := acc.get idx hidx }⟧ = (lexpr.mulRec rexpr curr).getLsbD idx
idx✝ : Nat
hidx✝ : idx✝ < w
res : RefVecEntry BVBit w
h✝ : curr + 1 < w
hconstant : aig.isConstant (rhs.get (curr + 1) h✝) false = true
hgo : go aig lhs rhs (curr + 1 + 1) acc = res
idx : Nat
hidx : idx < w
⊢ ⟦assign.toAIGAssignment, { aig := aig, ref := acc.get idx hidx }⟧ = (lexpr.mulRec rexpr (curr + 1)).getLsbD idx

Proof state:
case isTrue.isFalse
w : Nat
aig : AIG BVBit
curr : Nat
hcurr : curr + 1 ≤ w
acc lhs rhs : aig.RefVec w
lexpr rexpr : BitVec w
assign : Assignment
hleft :
  ∀ (idx : Nat) (hidx : idx < w), ⟦assign.toAIGAssignment, { aig := aig, ref := lhs.get idx hidx }⟧ = lexpr.getLsbD idx
hright :
  ∀ (idx : Nat) (hidx : idx < w), ⟦assign.toAIGAssignment, { aig := aig, ref := rhs.get idx hidx }⟧ = rexpr.getLsbD idx
hacc :
  ∀ (idx : Nat) (hidx : idx < w),
    ⟦assign.toAIGAssignment, { aig := aig, ref := acc.get idx hidx }⟧ = (lexpr.mulRec rexpr curr).getLsbD idx
idx : Nat
hidx : idx < w
res : RefVecEntry BVBit w
h✝¹ : curr + 1 < w
h✝ : ¬aig.isConstant (rhs.get (curr + 1) h✝¹) false = true
hgo :
  (let res := blastShiftLeftConst aig { vec := lhs, distance := curr + 1 };
    let aig_1 := res.aig;
    let shifted := res.vec;
    let_fun this := ⋯;
    let lhs_1 := lhs.cast this;
    let rhs_1 := rhs.cast this;
    let acc_1 := acc.cast this;
    let res := blastAdd aig_1 { lhs := acc_1, rhs := shifted };
    let aig_2 := res.aig;
    let added := res.vec;
    let_fun this_1 := ⋯;
    let lhs_2 := lhs_1.cast this_1;
    let rhs_2 := rhs_1.cast this_1;
    let acc_2 := acc_1.cast this_1;
    let res := RefVec.ite aig_2 { discr := rhs_2.get (curr + 1) h✝¹, lhs := added, rhs := acc_2 };
    let aig_3 := res.aig;
    let acc_3 := res.vec;
    let_fun this := ⋯;
    let lhs := lhs_2.cast this;
    let rhs := rhs_2.cast this;
    go aig_3 lhs rhs (curr + 1 + 1) acc_3) =
    res
⊢ ⟦assign.toAIGAssignment, { aig := res.aig, ref := res.vec.get idx hidx }⟧ = (lexpr.mulRec rexpr w).getLsbD idx

Tactic:
dsimp only at hgo

Result:
case isTrue.isFalse
w : Nat
aig : AIG BVBit
curr : Nat
hcurr : curr + 1 ≤ w
acc lhs rhs : aig.RefVec w
lexpr rexpr : BitVec w
assign : Assignment
hleft :
  ∀ (idx : Nat) (hidx : idx < w), ⟦assign.toAIGAssignment, { aig := aig, ref := lhs.get idx hidx }⟧ = lexpr.getLsbD idx
hright :
  ∀ (idx : Nat) (hidx : idx < w), ⟦assign.toAIGAssignment, { aig := aig, ref := rhs.get idx hidx }⟧ = rexpr.getLsbD idx
hacc :
  ∀ (idx : Nat) (hidx : idx < w),
    ⟦assign.toAIGAssignment, { aig := aig, ref := acc.get idx hidx }⟧ = (lexpr.mulRec rexpr curr).getLsbD idx
idx : Nat
hidx : idx < w
res : RefVecEntry BVBit w
h✝¹ : curr + 1 < w
h✝ : ¬aig.isConstant (rhs.get (curr + 1) h✝¹) false = true
hgo :
  go
      (RefVec.ite
          (blastAdd (blastShiftLeftConst aig { vec := lhs, distance := curr + 1 }).aig
              { lhs := acc.cast ⋯, rhs := (blastShiftLeftConst aig { vec := lhs, distance := curr + 1 }).vec }).aig
          { discr := ((rhs.cast ⋯).cast ⋯).get (curr + 1) h✝¹,
            lhs :=
              (blastAdd (blastShiftLeftConst aig { vec := lhs, distance := curr + 1 }).aig
                  { lhs := acc.cast ⋯, rhs := (blastShiftLeftConst aig { vec := lhs, distance := curr + 1 }).vec }).vec,
            rhs := (acc.cast ⋯).cast ⋯ }).aig
      (((lhs.cast ⋯).cast ⋯).cast ⋯) (((rhs.cast ⋯).cast ⋯).cast ⋯) (curr + 1 + 1)
      (RefVec.ite
          (blastAdd (blastShiftLeftConst aig { vec := lhs, distance := curr + 1 }).aig
              { lhs := acc.cast ⋯, rhs := (blastShiftLeftConst aig { vec := lhs, distance := curr + 1 }).vec }).aig
          { discr := ((rhs.cast ⋯).cast ⋯).get (curr + 1) h✝¹,
            lhs :=
              (blastAdd (blastShiftLeftConst aig { vec := lhs, distance := curr + 1 }).aig
                  { lhs := acc.cast ⋯, rhs := (blastShiftLeftConst aig { vec := lhs, distance := curr + 1 }).vec }).vec,
            rhs := (acc.cast ⋯).cast ⋯ }).vec =
    res
⊢ ⟦assign.toAIGAssignment, { aig := res.aig, ref := res.vec.get idx hidx }⟧ = (lexpr.mulRec rexpr w).getLsbD idx