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Proof step 3 from proof refine-read (previous step)

# lpt = # avol0 - sb.main, sb.main + # lpt0 = # avol0, subarray(avol0, sb.main, # lpt)[m] = mapped(buf1), avol0[0] = mapped(buf2), avol0[sb.orph] = mapped(buf3), avol0[sb.log] = mapped(buf4), buf = buf0, m < # lpt0, disk-layout(sb, # lpt0), ebm-vol-inv(subarray(avol0, sb.main, # lpt)), ebm-vol-inv(avol0), is-encoded(log, buf4), is-encoded(lpt, lebs(avol0, sb.lpt, lptlebs(# lpt, LEB_SIZE))), is-encoded(sb, buf2), is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# lpt0, LEB_SIZE))), is-encoded-pad(orphans, sb.orphsize, buf3), mapped-full?(avol0, sb.lpt, lptlebs(# lpt0, LEB_SIZE)), n + n0 ≤ # buf0, m0 + n0 ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf4 = logoff ⊦ ⟪persistence_io_read#(m, m0, n, n0, sb, avol0; buf; err)⟫ ⟨apersistence_io_read#(m, m0, n, n0, sb.indexaddr, sb.maxino, log, subarray(avol0, sb.main, # avol0 - sb.main), lpt, orphans; buf0; err0)⟩ (buf = buf0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# lpt = # avol0 - m6, m6 + # lpt0 = # avol0, avol0[m2] = mapped(buf4), avol0[m3] = mapped(buf3), avol0[0] = mapped(buf2), subarray(avol0, m6, # lpt)[m] = mapped(buf1), buf = buf0, sb = mksb(adr, m1, m2, m3, m4, m5, m6), m < # lpt0, disk-layout(sb, # lpt0), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-encoded(lpt0, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(sb, buf2), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans, m4, buf3), mapped-full?(avol0, m5, lptlebs(# lpt0, LEB_SIZE)), m0 + n0 ≤ LEB_SIZE, n + n0 ≤ # buf0, logoff ≠ LEB_SIZE → # buf4 = logoff ⊦ ⟪persistence_io_read#(m, m0, n, n0, sb, avol0; buf; err)⟫ ⟨apersistence_io_read#(m, m0, n, n0, adr, m1, log, subarray(avol0, m6, # avol0 - m6), lpt, orphans; buf0; err0)⟩ (buf = buf0 ∧ 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, m1, m2, m3, m4, m5, m6]

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, m1, m2, m3, m4, m5, m6