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Proof step 39 from proof prepost-init-vols-mappings (previous step)

# wlar = # apebs, avhdr.leb = VTBL_LNUM, avhdr0.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, avhdr.vol = VTBL_VOLID, wlar[n] = wl-entry(m0, used), wlar[n0] = wl-entry(m4, used), apebs[n0] = mkpeb(aechdr(m4), avhdr0, buf0, m1, false), apebs[n] = mkpeb(aehdr, avhdr, buf, m, false), recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(n0, m3), avhdr0.valid?, n < # apebs, n0 < # apebs, bflipset-cons(bflipset, wlar), is-encoded(to-vtbl(vols), buf), unique-sqns(apebs), unmapped-vols(vols), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), VTBL_VOLID × VTBL_LNUM ∈ recs0, n < # apebs → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ n0 = n, n ∈ q, VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
# wlar = # apebs, avhdr0.sqn = avhdr.sqn, avhdr.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(n0, m3), apebs[n] = mkpeb(aechdr(m0), avhdr, buf, m, false), apebs[n0] = mkpeb(aechdr(m4), avhdr0, buf0, m1, false), wlar[n0] = wl-entry(m4, used), wlar[n] = wl-entry(m0, used), avhdr0.valid?, n0 < # apebs, n < # apebs, bflipset-cons(bflipset, wlar), is-encoded(to-vtbl(vols), buf), unique-sqns(apebs), unmapped-vols(vols), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m0), avhdr, buf, m, false)), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), VTBL_VOLID × VTBL_LNUM ∈ recs0 ⊦ n0 = n, VTBL_VOLID ∈ vols, n ∈ q

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ free; (s)% ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ used ≠ erasing; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.vol = v; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.leb = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ used ≠ erroneous; (s)% ⊦ wl-entry(m, stat).status = stat; (s)