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Proof step 112 from proof prepost-init-vols-mappings (previous step)

# wlar0 = # wlar, # apebs = # wlar, apebs[m5] = mkpeb(aehdr1, avidhdr(v0, m1, m9, m10, m11), buf1, m12, false), wlar[m5, wl-entry(m7, erasing)][n0] = wl-entry(m8, stat0), recs1[v0 × m1] = 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), m1 < vtbl[v0], m5 < # wlar, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), is-encoded(vtbl, buf), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar0, q1), valid-eraseq(wlar, q), valid-eraseq-strong(apebs, vtbl, q), valid-eraseq-stronger(apebs, q1), valid-peb(mkpeb(aehdr1, avidhdr(v0, m1, m9, m10, m11), buf1, m12, false)), valid-peb(v0, m1, mkpeb(aehdr1, avidhdr(v0, m1, m9, m10, m11), buf1, m12, false)), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols0, wlar0, n), valid-vtbl(apebs, vols, wlar, n), valid-wl(apebs, wlar0), v0 ∈ vtbl, v0 × m1 ∈ recs1, q1 ⊆ q + eq-entry(m5, v0 × m1) ', q1 ⊆ q, recs1 ⊥ vols, m5 < # wlar → (wlar[m5].status = erroneous ↔ apebs[m5].bad) ∧ (wlar[m5].status = free → apebs[m5].vidhdr = empty) ∧ (wlar[m5].status ≠ erroneous ∧ wlar[m5].status ≠ erasing → apebs[m5].echdr = aechdr(wlar[m5].ec)) ∧ (wlar[m5].status = used → (∃ v, m. valid-peb(v, m, apebs[m5]) ∧ apebs[m5].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ m5 = n, recs1 = ∅, valid-eraseq-strong(apebs, vtbl, q + eq-entry(m5, v0 × m1) '), m5 ∈ q, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols, n ∈ q1, v0 ∈ vols ∧ m1 < # vols[v0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 113:
# wlar0 = # wlar, # apebs = # wlar, apebs[m5] = mkpeb(aechdr(m7), avidhdr(v1, m13, valid-sqns(v1, m13, apebs).max, m10, m11), 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(wlar, q), 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-peb(v1, m13, 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, 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 ⊦ 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]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ used ≠ free; (s)% ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ used ≠ erasing; (s)% ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ used ≠ erroneous; (s)% ⊦ wl-entry(m, stat).status = stat; (s)