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Proof step 3 from proof refine-add-log-leb (previous step)

# lpt = # avol - sb.main, sb.main + # lpt0 = # avol, avol[sb.log] = mapped(buf1), avol[sb.orph] = mapped(buf0), avol[0] = mapped(buf), avol0 = subarray(avol, sb.main, # lpt), disk-layout(sb, # lpt0), ebm-vol-inv(avol), ebm-vol-inv(subarray(avol, sb.main, # lpt)), is-encoded(lpt0, lebs(avol, sb.lpt, lptlebs(# lpt0, LEB_SIZE))), is-encoded(sb, buf), is-encoded(lpt, lebs(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE))), is-encoded(plog, buf1), is-encoded-pad(orphans, sb.orphsize, buf0), mapped-full?(avol, sb.lpt, lptlebs(# lpt0, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_add_log_leb#(m2, sb, EB_PAGE_SIZE, LEB_SIZE; logoff, avol; err)⟫ ⟨apersistence_io_add_log_leb#(m2, sb.indexaddr, sb.maxino, avol0, lpt, orphans; plog; err0)⟩ ( # avol = sb.main + (# avol - sb.main) ∧ avol0 = subarray(avol, sb.main, # avol - sb.main) ∧ is-encoded(plog, avol[sb.log].data) ∧ is-encoded(lpt, lebs(avol, sb.lpt, lptlebs(# avol - sb.main, LEB_SIZE))) ∧ is-encoded-pad(orphans, sb.orphsize, avol[sb.orph].data) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# lpt = # avol - m5, m5 + # lpt0 = # avol, avol[0] = mapped(buf), avol[m1] = mapped(buf0), avol[m0] = mapped(buf1), avol0 = subarray(avol, m5, # lpt), sb = mksb(adr, m, m0, m1, m3, m4, m5), disk-layout(sb, # lpt0), ebm-vol-inv(subarray(avol, m5, # lpt)), ebm-vol-inv(avol), is-encoded(plog, buf1), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(sb, buf), is-encoded(lpt0, lebs(avol, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt0, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_add_log_leb#(m2, sb, EB_PAGE_SIZE, LEB_SIZE; logoff, avol; err)⟫ ⟨apersistence_io_add_log_leb#(m2, adr, m, avol0, lpt, orphans; plog; err0)⟩ ( # avol = m5 + (# avol - m5) ∧ avol0 = subarray(avol, m5, # avol - m5) ∧ is-encoded(plog, avol[m0].data) ∧ is-encoded(lpt, lebs(avol, m4, lptlebs(# avol - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol[m1].data) ∧ 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] → [sb, adr, m, m1, m2, m3, m4, m5]

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: sb, adr, m, m1, m2, m3, m4, m5