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Proof step 14 from proof refine-commit (previous step)

# avol2 = # avol0, # avol0 = # lpt0 + sb0.main, # lpt = # lpt0, # lpt2 = # lpt0, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), avol2[0] = mapped(buf2), avol2[sb0.orph] = mapped(buf3), avol2[sb0.log] = mapped(buf4), subarray(avol2, sb0.main, # avol0 - sb0.main) = subarray(avol0, sb0.main, # avol0 - sb0.main), disk-layout(mksb(adr0, m0, m1, m2, m4, m5, sb0.main), # lpt0), disk-layout(sb0, # lpt0), ebm-vol-inv(avol2), ebm-vol-inv(subarray(avol0, sb0.main, # lpt0)), ebm-vol-inv(avol0), is-encoded(log, buf4), is-encoded(lpt0, lebs(avol2, sb0.lpt, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr0, m0, m1, m2, m4, m5, sb0.main), buf), is-encoded(lpt2, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(plog, buf1), is-encoded(sb0, buf2), is-encoded-pad(ns, m4, buf0), is-encoded-pad(orphans1, sb0.orphsize, buf3), mapped-full?(avol2, sb0.lpt, lptlebs(# lpt0, LEB_SIZE)), mapped-full?(avol0, m5, lptlebs(# lpt0, LEB_SIZE)), sb0.main ≤ # avol0, logoff0 ≠ LEB_SIZE → # buf4 = logoff0, err = ESUCCESS → sb0.indexaddr = adr1 ∧ sb0.maxino = m3 ∧ buf4 = mkbuf(0) ∧ is-encoded(lpt, lebs(avol2, sb0.lpt, lptlebs(# avol0 - sb0.main, LEB_SIZE))) ∧ orphans1 = ns0, err ≠ ESUCCESS → sb0 = mksb(adr0, m0, m1, m2, m4, m5, sb0.main) ∧ avol2[m1] = mapped(buf1) ∧ avol2[m2] = mapped(buf0) ∧ lebs(avol2, m5, lptlebs(# avol0 - sb0.main, LEB_SIZE)) = lebs(avol0, m5, lptlebs(# avol0 - sb0.main, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff, err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨apersistence_io_commit#(lpt, adr1, m3, subarray(avol0, sb0.main, # lpt0); ns0, adr0, m0, plog, lpt2, ns; err0)⟩ ( m0 = sb0.maxino ∧ adr0 = sb0.indexaddr ∧ subarray(avol0, sb0.main, # lpt0) = subarray(avol2, sb0.main, # avol0 - sb0.main) ∧ log = plog ∧ is-encoded(lpt2, lebs(avol2, sb0.lpt, lptlebs(# avol0 - sb0.main, LEB_SIZE))) ∧ orphans1 = ns ∧ orphans0 = ns0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
# lpt2 = # lpt0, # lpt = # lpt0, # avol0 = # lpt0 + m10, # avol2 = # avol0, avol2[m6] = mapped(buf4), avol2[m7] = mapped(buf3), avol2[0] = mapped(buf2), avol0[0] = mapped(buf), avol0[m2] = mapped(buf0), avol0[m1] = mapped(buf1), sb0 = mksb(adr, m, m6, m7, m8, m9, m10), subarray(avol2, m10, # avol0 - m10) = subarray(avol0, m10, # avol0 - m10), disk-layout(sb0, # lpt0), disk-layout(mksb(adr0, m0, m1, m2, m4, m5, m10), # lpt0), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m10, # lpt0)), ebm-vol-inv(avol2), is-encoded(sb0, buf2), is-encoded(plog, buf1), is-encoded(lpt2, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr0, m0, m1, m2, m4, m5, m10), buf), is-encoded(lpt0, lebs(avol2, m9, lptlebs(# lpt0, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans1, m8, buf3), is-encoded-pad(ns, m4, buf0), mapped-full?(avol0, m5, lptlebs(# lpt0, LEB_SIZE)), mapped-full?(avol2, m9, lptlebs(# lpt0, LEB_SIZE)), m10 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff, err ≠ ESUCCESS → sb0 = mksb(adr0, m0, m1, m2, m4, m5, m10) ∧ avol2[m1] = mapped(buf1) ∧ avol2[m2] = mapped(buf0) ∧ lebs(avol2, m5, lptlebs(# avol0 - m10, LEB_SIZE)) = lebs(avol0, m5, lptlebs(# avol0 - m10, LEB_SIZE)), err = ESUCCESS → adr = adr1 ∧ m = m3 ∧ buf4 = mkbuf(0) ∧ is-encoded(lpt, lebs(avol2, m9, lptlebs(# avol0 - m10, LEB_SIZE))) ∧ orphans1 = ns0, logoff0 ≠ LEB_SIZE → # buf4 = logoff0, err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨apersistence_io_commit#(lpt, adr1, m3, subarray(avol0, m10, # lpt0); ns0, adr0, m0, plog, lpt2, ns; err0)⟩ ( m0 = m ∧ adr0 = adr ∧ subarray(avol0, m10, # lpt0) = subarray(avol2, m10, # avol0 - m10) ∧ log = plog ∧ is-encoded(lpt2, lebs(avol2, m9, lptlebs(# avol0 - m10, LEB_SIZE))) ∧ orphans1 = ns ∧ orphans0 = ns0 ∧ err = err0)

Rule argument

spec: superblock name: elim seq: ⊦ ( ( ( ( (adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4) subst: [sb, adr, m, m0, m1, m2, m3, m4] → [sb0, adr, m, m6, m7, m8, m9, m10]

Additional information

Used simplifier rules: ⊦ ( ( ( ((adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4); (elim) Used terms: sb0, adr, m, m6, m7, m8, m9, m10