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Proof step 282 from proof inv-commit (previous step)

# avol = # avol0, # lpt0 = # lpt, # lebs(avol, 5, lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol[0] = mapped(buf2), avol[1] = mapped(mkbuf(0)), avol[2] = mapped(buf1), avol[3] = mapped(buf), avol[4] = mapped(buf0), avol0[0] = mapped(buf2), avol0[4] = mapped(buf0), avol0[2] = mapped(buf1), 3 < # avol0, ebm-vol-inv(avol), ebm-vol-inv(avol0[1, mapped(mkbuf(0))]), ebm-vol-inv(avol0), ebm-vol-inv(avol0[1, mapped(mkbuf(0))][3, mapped(buf)]), is-encoded(lpt, lebs(avol, 5, lptlebs(# lpt, LEB_SIZE))), 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)), buf2), is-encoded-pad(orphans0, m6, buf0), is-encoded-pad(orphans, # orphans, buf), mapped-full?(avol, 5, lptlebs(# lpt, LEB_SIZE)), mapped-full?(avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE)), range=(avol, 5 + lptlebs(# lpt, LEB_SIZE), avol0, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE) + # lpt), 5 ≤ # avol0, 5 + lptlebs(# lpt, LEB_SIZE) ≤ # avol0, 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?(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol, 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt1, LEB_SIZE)))

User applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: lpt0 abort: F discard: T computed: F

Additional information

Used simplifier rules: rangeeq-lebs: ⊦ range=(avol, n, avol0, n, m + m0) → lebs(avol, n, m) = lebs(avol0, n, m);% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + m = 2 * m; (s)% ⊦ m ≤ m + n; (s)%m ≤ n0, n0 + n1 ≤ m + m2 ⊦ range=(avol0, m, avol1, m, m2) ∧ mapped-full?(avol1, n0, n1) → mapped-full?(avol0, n0, n1); (ss) Used terms: lpt0