-- Mathlib/.lake/packages/lean4/src/lean/Std/Sat/AIG/If.lean
theorem go_decl_eq (aig : AIG α) (curr : Nat) (hcurr : curr ≤ w) (discr : Ref aig)
    (lhs rhs : RefVec aig w) (s : RefVec aig curr) :
    ∀ (idx : Nat) (h1) (h2),
      (go aig curr hcurr discr lhs rhs s).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
hcurr : curr ≤ w
discr : aig.Ref
lhs rhs : aig.RefVec w
s : aig.RefVec curr
res : RefVecEntry α w
hgo :
  (if hcurr : curr < w then
      let input := { discr := discr, lhs := lhs.get curr hcurr, rhs := rhs.get curr hcurr };
      let res := aig.mkIfCached input;
      let aig_1 := res.aig;
      let ref := res.ref;
      let_fun this := ⋯;
      let discr_1 := discr.cast this;
      let lhs_1 := lhs.cast this;
      let rhs_1 := rhs.cast this;
      let s := s.cast this;
      let s := s.push ref;
      go aig_1 (curr + 1) ⋯ discr_1 lhs_1 rhs_1 s
    else
      let_fun this := ⋯;
      { aig := aig, vec := this ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

Tactic:
dsimp only at hgo

Result:
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
discr : aig.Ref
lhs rhs : aig.RefVec w
s : aig.RefVec curr
res : RefVecEntry α w
hgo :
  (if hcurr : curr < w then
      go (aig.mkIfCached { discr := discr, lhs := lhs.get curr hcurr, rhs := rhs.get curr hcurr }).aig (curr + 1) ⋯
        (discr.cast ⋯) (lhs.cast ⋯) (rhs.cast ⋯)
        ((s.cast ⋯).push (aig.mkIfCached { discr := discr, lhs := lhs.get curr hcurr, rhs := rhs.get curr hcurr }).ref)
    else { aig := aig, vec := ⋯ ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]

Proof state:
case isTrue
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
discr : aig.Ref
lhs rhs : aig.RefVec w
s : aig.RefVec curr
res : RefVecEntry α w
h✝ : curr < w
hgo :
  go (aig.mkIfCached { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).aig (curr + 1) ⋯ (discr.cast ⋯)
      (lhs.cast ⋯) (rhs.cast ⋯)
      ((s.cast ⋯).push (aig.mkIfCached { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).ref) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size)
    (h2 :
      idx <
        (go (aig.mkIfCached { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).aig (curr + 1) ⋯
                (discr.cast ⋯) (lhs.cast ⋯) (rhs.cast ⋯)
                ((s.cast ⋯).push
                  (aig.mkIfCached
                      { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).ref)).aig.decls.size),
    (go (aig.mkIfCached { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).aig (curr + 1) ⋯
              (discr.cast ⋯) (lhs.cast ⋯) (rhs.cast ⋯)
              ((s.cast ⋯).push
                (aig.mkIfCached
                    { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).ref)).aig.decls[idx] =
      aig.decls[idx]

Tactic:
intro idx h1 h2

Result:
case isTrue
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
discr : aig.Ref
lhs rhs : aig.RefVec w
s : aig.RefVec curr
res : RefVecEntry α w
h✝ : curr < w
hgo :
  go (aig.mkIfCached { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).aig (curr + 1) ⋯ (discr.cast ⋯)
      (lhs.cast ⋯) (rhs.cast ⋯)
      ((s.cast ⋯).push (aig.mkIfCached { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).ref) =
    res
idx : Nat
h1 : idx < aig.decls.size
h2 :
  idx <
    (go (aig.mkIfCached { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).aig (curr + 1) ⋯
            (discr.cast ⋯) (lhs.cast ⋯) (rhs.cast ⋯)
            ((s.cast ⋯).push
              (aig.mkIfCached { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).ref)).aig.decls.size
⊢ (go (aig.mkIfCached { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).aig (curr + 1) ⋯
            (discr.cast ⋯) (lhs.cast ⋯) (rhs.cast ⋯)
            ((s.cast ⋯).push
              (aig.mkIfCached { discr := discr, lhs := lhs.get curr h✝, rhs := rhs.get curr h✝ }).ref)).aig.decls[idx] =
    aig.decls[idx]

Proof state:
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
discr : aig.Ref
lhs rhs : aig.RefVec w
s : aig.RefVec curr
res : RefVecEntry α w
hgo : go aig curr hcurr discr lhs rhs 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

Result:
α : Type
inst✝¹ : Hashable α
inst✝ : DecidableEq α
w : Nat
aig : AIG α
curr : Nat
hcurr : curr ≤ w
discr : aig.Ref
lhs rhs : aig.RefVec w
s : aig.RefVec curr
res : RefVecEntry α w
hgo :
  (if hcurr : curr < w then
      let input := { discr := discr, lhs := lhs.get curr hcurr, rhs := rhs.get curr hcurr };
      let res := aig.mkIfCached input;
      let aig_1 := res.aig;
      let ref := res.ref;
      let_fun this := ⋯;
      let discr_1 := discr.cast this;
      let lhs_1 := lhs.cast this;
      let rhs_1 := rhs.cast this;
      let s := s.cast this;
      let s := s.push ref;
      go aig_1 (curr + 1) ⋯ discr_1 lhs_1 rhs_1 s
    else
      let_fun this := ⋯;
      { aig := aig, vec := this ▸ s }) =
    res
⊢ ∀ (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < res.aig.decls.size), res.aig.decls[idx] = aig.decls[idx]