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Proof step 20 from proof refine-erase (previous step)

# apebs = # wlar, # apebs = # wlar0, vols[v][vtblpnum2] = ⌜n⌝ , lref = v × vtblpnum2, q = q0 + eq-entry(vtblpnum, lref), vtblpnum = vols[v][vtblpnum2].pnum, wlar = wlar0[vtblpnum, wlar0[vtblpnum].status:= erasing], avols[v][vtblpnum2].mapped?, vtblpnum < # wlar0, n < # wlar0, vtblpnum2 < # avols[v], vtblpnum2 < # vols[v], abs(avols, apebs, vols, q0), bflipset-cons(bflipset -- vols[v][vtblpnum2].pnum, wlar), bflipset-cons(bflipset, wlar0), ebm-cons(avols), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols[v, vols[v][vtblpnum2, unmapped]], vtblpnum1), valid-ebatbl(apebs, wlar0, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-eraseq(apebs, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-vtbl(apebs, vols, wlar0, vtblpnum1), valid-wl(apebs, wlar), valid-wl(apebs, wlar0), v ∈ avols, v ∈ vols ⊦ ⟪ubi_erase_all#(vols[v, vols[v][vtblpnum2, unmapped]], bflipset -- vols[v][vtblpnum2].pnum, vtblpnum1, sqnum; wlar, q, apebs; err)⟫ ⟨ebm_erase#(v, vtblpnum2; avols; err0)⟩ (abs(avols, apebs, vols[v, vols[v][vtblpnum2, unmapped]], q) ∧ err = err0), vols[v][vtblpnum2] = unmapped, VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols[v, vols[v][vtblpnum2, unmapped]]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# apebs = # wlar0, vols[v][vtblpnum2] = ⌜n⌝ , q = q0 + eq-entry(n, v × vtblpnum2) ', wlar = wlar0[n, wl-entry(wlar0[n].ec, erasing)], avols[v][vtblpnum2].mapped?, vtblpnum2 < # vols[v], vtblpnum2 < # avols[v], n < # wlar0, abs(avols, apebs, vols, q0), bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset -- n, wlar0), ebm-cons(avols), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols, vtblpnum1), valid-ebatbl(apebs, wlar0[n, wl-entry(wlar0[n].ec, erasing)], vols[v, vols[v][vtblpnum2, unmapped]], vtblpnum1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq(apebs, q0 + eq-entry(n, v × vtblpnum2) '), valid-eraseq(wlar0[n, wl-entry(wlar0[n].ec, erasing)], q0 + eq-entry(n, v × vtblpnum2) '), valid-eraseq(q0 + eq-entry(n, v × vtblpnum2) '), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar0, vtblpnum1), valid-vtbl(apebs, vols, wlar0[n, wl-entry(wlar0[n].ec, erasing)], vtblpnum1), valid-wl(apebs, wlar0), valid-wl(apebs, wlar0[n, wl-entry(wlar0[n].ec, erasing)]), v ∈ vols, v ∈ avols, ¬ VTBL_VOLID ∈ vols ⊦ ⟪ubi_erase_all#(vols[v, vols[v][vtblpnum2, unmapped]], bflipset -- vols[v][vtblpnum2].pnum, vtblpnum1, sqnum; wlar, q, apebs; err)⟫ ⟨ebm_erase#(v, vtblpnum2; avols; err0)⟩ (abs(avols, apebs, vols[v, vols[v][vtblpnum2, unmapped]], q) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ eqent ∈ eqent0 ' ↔ eqent = eqent0; (s)% ⊦ eqent ∈ q + q0 ↔ eqent ∈ q ∨ eqent ∈ q0; (s)% ⊦ unmapped ≠ ⌜m⌝ ; (s)% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]%in-15: ⊦ q + eqent ' = q0 → eqent ∈ q0; (forward) from specification list[erasequeue-base]% ⊦ v ∈ vols[v0, ebatbl] ↔ v = v0 ∨ v ∈ vols; (ws)% ⊦ n ∈ ns -- n0 ↔ n ≠ n0 ∧ n ∈ ns; (s)%wle.status ≠ used ⊦ bflipset-cons(bflipset, wlar[m, wle]) ↔ bflipset-cons(bflipset, wlar) ∧ ¬ m ∈ bflipset; (s)% ⊦ used ≠ erasing; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ ⌜m⌝ .pnum = m; (s)% ⊦ # wlar[n, wle] = # wlar; (s)% ⊦ wle.status:= stat = wl-entry(wle.ec, stat); (s)% ⊦ q + eqent = q + eqent '; (s)