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Proof step 115 from proof prepost-init-vols-mappings (previous step)

# apebs = # wlar, # wlar0 = # wlar, wlar[m5] = wl-entry(m7, used), recs1[v × m0] = recovery-entry(m3, m4), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), recs1[v1 × m13] = recovery-entry(m5, m6), wlar[m5, wl-entry(m7, erasing)][n0] = wl-entry(m8, stat0), apebs[m5] = mkpeb(aechdr(m7), avidhdr(v1, m13, valid-sqns(v1, m13, apebs).max, m10, m11), buf1, m12, false), mkpeb(aechdr(m7), avidhdr(v1, m13, valid-sqns(v1, m13, apebs).max, m10, m11), buf1, m12, false).echdr.valid?, m13 < vtbl[v1], m5 < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), is-encoded(vtbl, buf), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar, q), 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, m10, m11), buf1, m12, false)), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols, wlar, n), valid-vtbl(apebs, vols0, wlar0, n), valid-wl(apebs, wlar0), v1 × m13 ∈ recs1, v1 ∈ vtbl, q1 ⊆ q, q1 ⊆ q + eq-entry(m5, v1 × m13) ', recs1 ⊥ vols, ∃ m0, m1, m2. mkpeb(aechdr(m7), avidhdr(v1, m13, valid-sqns(v1, m13, apebs).max, m10, m11), buf1, m12, false).vidhdr = avidhdr(v1, m13, m0, m1, m2) ∧ ( m1 ≠ 0 → m1 ≤ datasize(mkpeb(aechdr(m7), avidhdr(v1, m13, valid-sqns(v1, m13, apebs).max, m10, m11), buf1, m12, false).data) ∧ m2 = checksum(mkpeb(aechdr(m7), avidhdr(v1, m13, valid-sqns(v1, m13, apebs).max, m10, m11), buf1, m12, false).data, m1)) ⊦ m5 = n, recs1 = ∅, mkpeb(aechdr(m7), avidhdr(v1, m13, valid-sqns(v1, m13, apebs).max, m10, m11), buf1, m12, false).bad, valid-eraseq-strong(apebs, vtbl, q + eq-entry(m5, v1 × m13) '), n ∈ q1, VTBL_VOLID ∈ vols, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols0, m5 ∈ q, v1 ∈ vols ∧ m13 < # vols[v1]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 116:
# apebs = # wlar, # wlar0 = # wlar, wlar[m5] = wl-entry(m7, used), recs1[v × m0] = recovery-entry(m3, m4), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), recs1[v1 × m13] = recovery-entry(m5, m6), wlar[m5, wl-entry(m7, erasing)][n0] = wl-entry(m8, stat0), apebs[m5] = mkpeb(aechdr(m7), avidhdr(v1, m13, valid-sqns(v1, m13, apebs).max, m9, m1), buf1, m12, false), m13 < vtbl[v1], m5 < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), is-encoded(vtbl, buf), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar, q), 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, vols, wlar, n), valid-vtbl(apebs, vols0, wlar0, n), valid-wl(apebs, wlar0), v1 × m13 ∈ recs1, v1 ∈ vtbl, q1 ⊆ q, q1 ⊆ q + eq-entry(m5, v1 × m13) ', 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) '), n ∈ q1, VTBL_VOLID ∈ vols, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols0, m5 ∈ q, v1 ∈ vols ∧ m13 < # vols[v1]

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ aechdr(m).valid?; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)%⊦ avidhdr(v, m, m0, m1, m2) = avidhdr(v0, m3, m4, m5, m6) ↔ v = v0 ∧ m = m3 ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)