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Proof step 39 from proof vols-is-max-is-min-eraseq (previous step)

# apebs = # wlar1, # wlar0 = # wlar1, wlar1[n] = wl-entry(m5, stat), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m4, stat = erroneous), wlar0[n] = wl-entry(m3, erasing), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), n < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar1), is-encoded(vtbl, buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, n0), valid-ebatbl(apebs, wlar1, vols1, m0), valid-eraseq(apebs, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, vtbl, q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-vtbl(apebs, vols0, wlar0, n0), valid-vtbl(apebs, vols1, wlar1, m0), valid-wl(apebs, wlar0), eq-entry(n, v0 × n2) ∈ q0, n ∈ q0, stat = free → avhdr0 = empty, stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m5), stat = used → valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m4, false)) ∧ avhdr0.sqn = valid-sqns(v, m, apebs).max, ∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])) ⊦ valid-eraseq-strong(apebs, to-vtbl(vols0), q0), VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1, v0 × n2 ∈ q1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-vtbl seq: ⊦ valid-vtbl(apebs, vols, wlar, n0) ↔ n0 < # apebs ∧ n0 < # wlar ∧ wlar[n0].status = used ∧ apebs[n0].vidhdr.vol = VTBL_VOLID ∧ apebs[n0].vidhdr.leb = VTBL_LNUM ∧ is-encoded(to-vtbl(vols), apebs[n0].data) subst: [n0, wlar, vols, apebs] → [n0, wlar0, vols0, apebs] flags: <all paths>

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ is-encoded(vtbl0, buf) → (is-encoded(vtbl1, buf) ↔ vtbl0 = vtbl1); (s) Used terms: n0, wlar0, vols0, apebs