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Proof step 9 from proof refine-commit (previous step)

# avol0 = # lpt1 + m6, # lpt = # lpt1, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), avol = subarray(avol0, m6, # lpt1), orphans = ns0, sb = mksb(adr0, m0, m1, m2, m4, m5, m6), disk-layout(mksb(adr0, m0, m1, m2, m4, m5, m6), # lpt1), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt1)), is-encoded(mksb(adr0, m0, m1, m2, m4, m5, m6), buf), is-encoded(lpt1, lebs(avol0, m5, lptlebs(# lpt1, LEB_SIZE))), is-encoded(plog, buf1), is-encoded-pad(ns, m4, buf0), mapped-full?(avol0, m5, lptlebs(# lpt1, LEB_SIZE)), m6 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ (∃ lpt, log, orphans. persistence-io-inv(sb, logoff, avol0, lpt, log, orphans)) ∧ EB_PAGE_SIZE = EB_PAGE_SIZE ∧ LEB_SIZE = LEB_SIZE ∧ ebm-vol-inv(avol0) ∧ # lpt + sb.main = # avol0 ∧ orphans = orphans ∧ sb = sb ∧ avol0 = avol0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# avol0 = # lpt1 + m6, # lpt = # lpt1, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), disk-layout(mksb(adr0, m0, m1, m2, m4, m5, m6), # lpt1), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt1)), is-encoded(mksb(adr0, m0, m1, m2, m4, m5, m6), buf), is-encoded(lpt1, lebs(avol0, m5, lptlebs(# lpt1, LEB_SIZE))), is-encoded(plog, buf1), is-encoded-pad(ns, m4, buf0), mapped-full?(avol0, m5, lptlebs(# lpt1, LEB_SIZE)), m6 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ∃ lpt0. m6 + # lpt0 = # avol0 ∧ mapped-full?(avol0, m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE)))

Rule argument

Additional information

Used simplifier rules: ⊦ 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)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (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%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).orph = m1; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).orphsize = m2; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).log = m0; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).lpt = m3; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (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)