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Proof step 327 from proof inv-commit (previous step)

# lpt0 = # lpt, # avol1 = # avol0, (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol0[0] = mapped(buf), avol0[4] = mapped(buf0), avol0[2] = mapped(buf1), 3 < # avol0, ebm-vol-inv(avol0[1, mapped(mkbuf(0))]), ebm-vol-inv(avol0), ebm-vol-inv(avol1), id○(avol1, avol0[1, mapped(mkbuf(0))], 3), is-encoded(log, buf1), is-encoded(lpt0, lebs(avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr0, m2, 2, 4, m6, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)), 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, ⌊err⌋ , logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ (∃ lpt1. lptlebs(# lpt, LEB_SIZE) = lptlebs(# lpt1, LEB_SIZE) ∧ 2 * lptlebs(# lpt, LEB_SIZE) = 2 * lptlebs(# lpt1, LEB_SIZE) ∧ (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt1 = # avol0 ∧ mapped-full?(avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol1, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)))) ∧ lebs(avol1, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE)) = lebs(avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 328:
# avol1 = # avol0, # lpt0 = # lpt, # avol0 = n0 + 5 + 2 * lptlebs(# lpt, LEB_SIZE), (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol0[2] = mapped(buf1), avol0[4] = mapped(buf0), avol0[0] = mapped(buf), 3 < # avol0, ebm-vol-inv(avol1), ebm-vol-inv(avol0), ebm-vol-inv(avol0[1, mapped(mkbuf(0))]), id○(avol1, avol0[1, mapped(mkbuf(0))], 3), is-encoded(mksb(adr0, m2, 2, 4, m6, 5 + lptlebs(# lpt, LEB_SIZE), 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf), is-encoded(lpt0, lebs(avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)), 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, ⌊err⌋ , logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ (∃ lpt1. lptlebs(# lpt, LEB_SIZE) = lptlebs(# lpt1, LEB_SIZE) ∧ 2 * lptlebs(# lpt, LEB_SIZE) = 2 * lptlebs(# lpt1, LEB_SIZE) ∧ (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt1 = # avol0 ∧ mapped-full?(avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol1, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)))) ∧ lebs(avol1, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(n0, LEB_SIZE)) = lebs(avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(n0, LEB_SIZE))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol0, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol0, n