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Proof step 7 from proof refine-commit (previous step)

# lpt = # lpt1, # avol0 = # lpt1 + m6, avol0[0] = mapped(buf), avol0[m2] = mapped(buf0), avol0[m1] = mapped(buf1), 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(subarray(avol0, m6, # lpt1)), ebm-vol-inv(avol0), is-encoded(plog, buf1), is-encoded(lpt1, lebs(avol0, m5, lptlebs(# lpt1, LEB_SIZE))), is-encoded(mksb(adr0, m0, m1, m2, m4, m5, m6), buf), 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, lpt1, 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(lpt1, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ is-encoded-pad(ns, sb.orphsize, avol0[sb.orph].data) ∧ orphans = ns0 ∧ err = err0)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: persistence-io-asm name: inv-commit seq: ∃ lpt, log, orphans. persistence-io-inv(sb, logoff, avol, lpt, log, orphans), m = EB_PAGE_SIZE, m0 = LEB_SIZE, ebm-vol-inv(avol), # lpt + sb.main = # avol, ns = orphans, sb0 = sb, avol0 = avol ⊦ ⟪persistence_io_commit# (lpt, adr, m1, m, m0; orphans, sb, avol, logoff; err)⟫ ( (∃ lpt, log, orphans. persistence-io-inv (sb, logoff, avol, lpt, log, orphans)) ∧ ebm-vol-inv(avol) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb.indexaddr = adr ∧ sb.maxino = m1 ∧ is-encoded([], avol[sb.log].data) ∧ is-encoded (lpt, lebs (avol, sb.lpt, lptlebs(# avol - sb.main, LEB_SIZE))) ∧ is-encoded-pad(ns, sb.orphsize, avol[sb.orph].data)) ∧ ( err ≠ ESUCCESS → sb = sb0 ∧ avol[sb.log] = avol0[sb.log] ∧ avol[sb.orph] = avol0[sb.orph] ∧ lebs (avol, sb.lpt, lptlebs(# avol - sb.main, LEB_SIZE)) = lebs (avol0, sb.lpt, lptlebs(# avol - sb.main, LEB_SIZE))) ∧ sb.main = sb0.main ∧ # avol = # avol0 ∧ subarray(avol, sb.main, # avol - sb.main) = subarray(avol0, sb.main, # avol - sb.main)) subst: [m0, m, m1, adr, lpt, logoff, avol, sb, orphans, err, ns, sb0, avol0] → [LEB_SIZE, EB_PAGE_SIZE, m3, adr1, lpt, logoff, avol0, sb, orphans, err, orphans, sb, avol0] flags: <all paths>

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