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Proof step 109 from proof refine-read-buf (previous step)

# buf3 = n5 + n1, # avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, n1 + n5 = n4 + min(n1, n2), m0 + n3 + n2 = LEB_SIZE, avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf4 + subarray(buf2, 0, n2 + (m0 - # buf4))), # buf4 < m0, m0 < EB_PAGE_SIZE + # buf4, m2 < # avol1, n2 + (m0 - # buf4) < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf4, EB_PAGE_SIZE), n1 ≤ n2 + n3, m0 + min(n1, n2) ≤ EB_PAGE_SIZE + # buf4, # buf4 ≤ LEB_SIZE, # buf4 ≤ m0 + n1, min(n1, n2) ≤ n1 + n5 ⊦ subarray(buf2, m0 - # buf4, min(n1, n2)) + subarray(mkempbuf(n1) + subarray(buf3, n1, n5), min(n1, n2), n4) = subarray(subarray(buf2, 0, n2 + (m0 - # buf4)) + mkempbuf(n3), m0 - # buf4, n1) + subarray(buf3, n1, n5), EB_PAGE_SIZE = 1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 110:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf3 = n5 + n1, m0 + n3 + n2 = LEB_SIZE, n1 + n5 = n4 + min(n1, n2), avol1[m2] = mapped(buf4 + subarray(buf2, 0, n2 + n0)), avol0[m2] = mapped(buf4), m0 = n0 + # buf4, n2 + n0 < EB_PAGE_SIZE, m2 < # avol1, m0 < EB_PAGE_SIZE + # buf4, # buf4 < m0, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf4, EB_PAGE_SIZE), min(n1, n2) ≤ n1 + n5, # buf4 ≤ m0 + n1, # buf4 ≤ LEB_SIZE, m0 + min(n1, n2) ≤ EB_PAGE_SIZE + # buf4, n1 ≤ n2 + n3, # buf4 ≤ m0 ⊦ subarray(buf2, n0, min(n1, n2)) + subarray(mkempbuf(n1) + subarray(buf3, n1, n5), min(n1, n2), n4) = subarray(subarray(buf2, 0, n2 + n0) + mkempbuf(n3), n0, n1) + subarray(buf3, n1, n5), EB_PAGE_SIZE = 1

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [# buf4, m0, n]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ min(n, m) < n ↔ min(n, m) = m ∧ m < n; (ws)% ⊦ n1 < n0 → min(n0, n1) = n1; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf4, m0, n