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Proof step 126 from proof inv-commit (previous step)

# avol = # avol0, # buf3 = lptsize(# lpt, LEB_SIZE), # lpt0 = # lpt, # buf3 = lptlebs(# lpt, LEB_SIZE) * LEB_SIZE, # avol0 = n0 + 2 * lptlebs(# lpt, LEB_SIZE) + 5, (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol0[0] = mapped(buf2), avol0[3] = mapped(buf0), avol0[1] = mapped(buf1), 4 < # avol0, 2 < # avol0, ebm-vol-inv(avol), ebm-vol-inv(avol0[2, mapped(mkbuf(0))]), ebm-vol-inv(avol0), ebm-vol-inv(avol0[2, mapped(mkbuf(0))][4, mapped(buf)]), is-encoded(lpt, buf3), is-encoded(log, buf1), is-encoded(lpt0, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf2), is-encoded-pad(orphans0, m6, buf0), is-encoded-pad(orphans, # orphans, buf), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), range=(avol, 0, avol0[2, mapped(mkbuf(0))][4, mapped(buf)], 0, 5 + lptlebs(# lpt, LEB_SIZE)), range=(avol, 5 + 2 * lptlebs(# lpt, LEB_SIZE), avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE), n0), 2 * lptlebs(# lpt, LEB_SIZE) + 5 ≤ # avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, ⌊err⌋ , logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ (∃ lpt1. 2 * lptlebs(# lpt, LEB_SIZE) = 2 * lptlebs(# lpt1, LEB_SIZE) ∧ (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt1 = # avol0 ∧ mapped-full?(avol, 5, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol, 5, lptlebs(# lpt1, LEB_SIZE)))) ∧ lebs(avol, 5, lptlebs(# avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE)) = lebs(avol0, 5, lptlebs(# avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 127:
# avol = # avol0, # buf3 = lptsize(# lpt, LEB_SIZE), # lpt0 = # lpt, # buf3 = lptlebs(# lpt, LEB_SIZE) * LEB_SIZE, (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol0[0] = mapped(buf2), avol0[3] = mapped(buf0), avol0[1] = mapped(buf1), 4 < # avol0, 2 < # avol0, ebm-vol-inv(avol), ebm-vol-inv(avol0[2, mapped(mkbuf(0))]), ebm-vol-inv(avol0), ebm-vol-inv(avol0[2, mapped(mkbuf(0))][4, mapped(buf)]), is-encoded(lpt, buf3), is-encoded(log, buf1), is-encoded(lpt0, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf2), is-encoded-pad(orphans0, m6, buf0), is-encoded-pad(orphans, # orphans, buf), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), range=(avol, 0, avol0[2, mapped(mkbuf(0))][4, mapped(buf)], 0, 5 + lptlebs(# lpt, LEB_SIZE)), range=(avol, 5 + 2 * lptlebs(# lpt, LEB_SIZE), avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt), 2 * lptlebs(# lpt, LEB_SIZE) + 5 ≤ # avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, ⌊err⌋ , logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ (∃ lpt1. 2 * lptlebs(# lpt, LEB_SIZE) = 2 * lptlebs(# lpt1, LEB_SIZE) ∧ (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt1 = # avol0 ∧ mapped-full?(avol, 5, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol, 5, lptlebs(# lpt1, LEB_SIZE)))) ∧ lebs(avol, 5, lptlebs(# avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE)) = lebs(avol0, 5, lptlebs(# avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE))

Rule argument

Additional information

Used simplifier rules: n < n0 ⊦ (* n) < m0 + (* n0); (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic