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Proof step 18 from proof inv-unmap (previous step)

m5 + # lpt = # avol, avol[0] = mapped(buf), avol[m2] = mapped(buf0), avol[m1] = mapped(buf1), m6 < # lpt, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol[m5 + m6, unmapped]), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ 0 = m5 + m6, m1 = m5 + m6, ∃ lpt0. m5 + # lpt0 = # avol ∧ mapped-full?(avol[m5 + m6, unmapped], m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol[m5 + m6, unmapped], m4, lptlebs(# lpt0, LEB_SIZE)))

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 3 terms: lpt

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%⊦ disk-layout(mksb(adr, m0, m1, m2, m, m3, m4), mainareasize) → ¬ m4 + n < m3 + lptlebs(mainareasize, LEB_SIZE); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n + m ≤ n0 ⊦ mapped-full?(avol[n0, aleb], n, m) ↔ mapped-full?(avol, n, m); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)%n + m ≤ n0, n + m ≤ # avol ⊦ lebs(avol[n0, aleb], n, m) = lebs(avol, n, m); (s) Used terms: lpt