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Proof step 6 from proof refine-commit (previous step)

# lpt = # lpt0, # lpt0 = n0, # avol0 = n0 + m6, m6 + # lpt1 = # avol0, avol0[0] = mapped(buf), avol0[m2] = mapped(buf0), avol0[m1] = mapped(buf1), avol = subarray(avol0, m6, # lpt0), 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(subarray(avol0, m6, # lpt0)), ebm-vol-inv(avol0), is-encoded(plog, buf1), is-encoded(lpt0, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr0, m0, m1, m2, m4, m5, m6), buf), is-encoded(lpt1, lebs(avol0, m5, lptlebs(# lpt1, LEB_SIZE))), is-encoded-pad(ns, m4, buf0), mapped-full?(avol0, m5, lptlebs(# lpt1, LEB_SIZE)), m6 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_commit#(lpt, adr1, m3, EB_PAGE_SIZE, LEB_SIZE; orphans, sb, avol0, logoff; err)⟫ ⟨apersistence_io_commit#(lpt, adr1, m3, avol; ns0, adr0, m0, plog, lpt0, ns; err0)⟩ ( m0 = sb.maxino ∧ adr0 = sb.indexaddr ∧ # avol0 = sb.main + (# avol0 - sb.main) ∧ avol = subarray(avol0, sb.main, # avol0 - sb.main) ∧ is-encoded(plog, avol0[sb.log].data) ∧ is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ is-encoded-pad(ns, sb.orphsize, avol0[sb.orph].data) ∧ orphans = ns0 ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ is-encoded(lpt0, buf) ∧ # lpt0 = # lpt1 → (is-encoded(lpt1, buf) ↔ lpt0 = lpt1); (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