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Proof step 171 from proof refine-write-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), avol1[m4] = mapped(buf2 + subarray(buf1, 0, m2)), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, m4 < # avol1, m2 < EB_PAGE_SIZE, n1 < n0, n1 < # buf3, n < m2 + n1, n < m2 + n0, n < n0 + m2, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(n1 + m2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(# buf2, EB_PAGE_SIZE), m2 ≤ n, n0 ≤ # buf3, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, # buf2 + n0 + m2 ≤ LEB_SIZE, (# buf2 + m2) + n3 ≤ LEB_SIZE, ⌊err1⌋ ⊦ subarray(buf3, 0, n1)[n - m2] = subarray(buf3, 0, n0)[n - m2], n1 = 0, n3 = 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: [m, n, n0] → [n, m2, n2]

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ 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)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ n + 0 = n; (s)%n ≠ 0, m % n = 0 ⊦ align↓(m, n) = m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, m2, n2