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Proof step 120 from proof prepost-init-vols-mappings (previous step)

# wlar0 = # wlar, # apebs = # wlar, m4 ∈ q ↔ m4 < # wlar ∧ wlar[m4].status = erasing, apebs[m5] = mkpeb(aechdr(m7), avidhdr(v1, m13, valid-sqns(v1, m13, apebs).max, m9, m1), buf1, m12, false), wlar[m5, wl-entry(m7, erasing)][n0] = wl-entry(m8, stat0), recs1[v1 × m13] = recovery-entry(m5, m6), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs1[v × m0] = recovery-entry(m3, m4), wlar[m5] = wl-entry(m7, used), m5 < # wlar, m13 < vtbl[v1], bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), is-encoded(vtbl, buf), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar0, q1), valid-eraseq-strong(apebs, vtbl, q), valid-eraseq-stronger(apebs, q1), valid-peb(mkpeb(aechdr(m7), avidhdr(v1, m13, valid-sqns(v1, m13, apebs).max, m9, m1), buf1, m12, false)), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols0, wlar0, n), valid-vtbl(apebs, vols, wlar, n), valid-wl(apebs, wlar0), v1 ∈ vtbl, v1 × m13 ∈ recs1, q1 ⊆ q + eq-entry(m5, v1 × m13) ', q1 ⊆ q, recs1 ⊥ vols, m9 ≠ 0 → m9 ≤ datasize(buf1) ∧ m1 = checksum(buf1, m9) ⊦ m5 = n, recs1 = ∅, valid-eraseq-strong(apebs, vtbl, q + eq-entry(m5, v1 × m13) '), m5 ∈ q, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols, n ∈ q1, v1 ∈ vols ∧ m13 < # vols[v1]

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] → [n, wlar, vols, 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)% ⊦ v ∈ to-vtbl(vols) ↔ v ∈ vols; (s)% ⊦ v ∈ vols → to-vtbl(vols)[v] = # vols[v]; (s) Used terms: n, wlar, vols, apebs