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Proof step 6 from proof recovery (previous step)

# lpt0 = # avol2, # avol0 = sb.main + # avol2, adr0 = sb.indexaddr, adr1 = adr2, avol1 = avol1, avol2 = subarray(avol0, sb.main, # avol0 - sb.main), avol4 = avol1, log1 = log2, lpt1 = lpt2, m0 = sb.maxino, m2 = EB_PAGE_SIZE, m3 = LEB_SIZE, m4 = m5, orphans = ns1, ebm-vol-inv(avol0), ebm-vol-inv(avol2), is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# avol2, LEB_SIZE))), is-encoded(log0, avol0[sb.log].data), is-encoded-pad(ns0, sb.orphsize, avol0[sb.orph].data), avol0 ⊆ avol1, ∃ lpt1, log1, orphans. persistence-io-inv(sb, m1, avol0, lpt1, log1, orphans) ⊦ avol0 ⊆ avol1 ∧ (∃ lpt, log, orphans. persistence-io-inv(sb, m1, avol0, lpt, log, orphans)) ∧ m2 = EB_PAGE_SIZE ∧ m3 = LEB_SIZE ∧ ebm-vol-inv(avol0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# lpt0 = # avol0 - sb.main, sb.main + # lpt = # avol0, avol0[sb.log] = mapped(buf1), avol0[sb.orph] = mapped(buf0), avol0[0] = mapped(buf), disk-layout(sb, # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, sb.main, # lpt0)), is-encoded(lpt, lebs(avol0, sb.lpt, lptlebs(# lpt, LEB_SIZE))), is-encoded(sb, buf), is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# lpt0, LEB_SIZE))), is-encoded(log0, buf1), is-encoded-pad(ns0, sb.orphsize, buf0), mapped-full?(avol0, sb.lpt, lptlebs(# lpt, LEB_SIZE)), avol0 ⊆ avol1, m1 ≠ LEB_SIZE → # buf1 = m1 ⊦ ∃ lpt1. sb.main + # lpt1 = # avol0 ∧ mapped-full?(avol0, sb.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol0, sb.lpt, lptlebs(# lpt1, LEB_SIZE)))

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)%m = n ⊦ disk-layout(sb, m) → disk-layout(sb, n); (s)%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)%⊦ persistence-io-inv(sb, logoff, avol, lpt, log, orphans) ↔ (∃ mainareasize. disk-layout(sb, mainareasize) ∧ sb.main + mainareasize = # avol ∧ avol[0].mapped? ∧ is-encoded(sb, avol[0].data) ∧ avol[sb.orph].mapped? ∧ is-encoded-pad(orphans, sb.orphsize, avol[sb.orph].data) ∧ avol[sb.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[sb.log].data = logoff) ∧ is-encoded(log, avol[sb.log].data) ∧ mapped-full?(avol, sb.lpt, lptlebs(mainareasize, LEB_SIZE)) ∧ # lpt = mainareasize ∧ is-encoded (lpt, lebs(avol, sb.lpt, lptlebs(mainareasize, LEB_SIZE)))); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ # subarray(avol, m, n) = n; (s)