| # 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), ebm-vol-inv(avol0[1, unmapped]), ebm-vol-inv(avol0), 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, ⌊err0⌋ , 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(avol0[1, unmapped], 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)))) ∧ lebs(avol0[1, unmapped], 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(n0, LEB_SIZE)) = lebs(avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(n0, LEB_SIZE)) |
# lpt0 = # lpt, (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol0[2] = mapped(buf1), avol0[4] = mapped(buf0), avol0[0] = mapped(buf), ebm-vol-inv(avol0[1, unmapped]), ebm-vol-inv(avol0), 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, ⌊err0⌋ , 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(avol0[1, unmapped], 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)))
Used simplifier rules: n0 < n, n + m ≤ # avol ⊦ lebs(avol[n0, aleb], n, m) = lebs(avol, n, m); (s)% ⊦ m + m = 2 * m; (s)%n < n0 ⊦ (* n) ≠ m0 + (* n0); (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)%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