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Proof step 293 from proof refine-read-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, LEB_SIZE = n0 + # buf, avol0[m2] = mapped(buf), avol1[m2] = mapped(buf1), m4 + 1 < n2 + min(n1, m4 - n2), n2 < EB_PAGE_SIZE, m2 < # avol1, m4 < EB_PAGE_SIZE, EB_PAGE_SIZE < n2 + min(n1, m4 - n2), m4 < n2 + min(n1, m4 - n2), abs(avol1, buffered(m2), mkwbuf(buf2, m6, m4), avol0, rofs), awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), min(n1, m4 - n2) ≤ # buf3, m6 ≤ # buf, # buf ≤ LEB_SIZE, (n2 + m6) + n1 ≤ LEB_SIZE, n1 ≤ # buf3, n2 ≤ m4, m6 ≤ LEB_SIZE, ¬ rofs → # buf = m6 ⊦ m4 = 0, min(n1, m4 - n2) = 1, min(n1, m4 - n2) = 0, n2 = 0

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [n2, m4, n]

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ m < min(n, m); (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n2, m4, n