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Proof step 181 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n3 + n5 + n1 = # buf3, min(n1, n2) + n4 = n1 + n5, LEB_SIZE = n0 + # buf0 + # buf, avol1[m2] = mapped(buf0 + buf), avol0[m2] = mapped(buf0 + buf), subarray(buf2, 0, n2) = subarray(buf, n3, n2), n6 < n5 + n1, n3 < n0 + # buf, (n3 + # buf0) + n2 < LEB_SIZE, # buf0 < LEB_SIZE, n2 < EB_PAGE_SIZE, m2 < # avol1, n3 < # buf, n3 + n2 < # buf, n3 < # buf3, n6 < n1 + n5, min(n1, n2) < n1 + n5, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), n1 + n3 ≤ # buf + n0, min(n1, n2) ≤ EB_PAGE_SIZE, min(n1, n2) ≤ n6 ⊦ subarray(subarray(buf + mkempbuf(n0), 0, n1 + n3) + subarray(buf3, n1 + n3, n5), n3 + min(n1, n2), n4)[n6 - min(n1, n2)] = (n6 < n1 ⊃ (buf + mkempbuf(n0))[n6 + n3];subarray(buf3, n1 + n3, n5)[n6 - n1]), n4 = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 182:
# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, min(n1, n2) + n4 = n1 + n5, n3 + n5 + n1 = # buf3, LEB_SIZE = n0 + # buf0 + # buf, avol0[m2] = mapped(buf0 + buf), avol1[m2] = mapped(buf0 + buf), n6 = n7 + min(n1, n2), subarray(buf2, 0, n2) = subarray(buf, n3, n2), min(n1, n2) < n1 + n5, n6 < n1 + n5, n3 < # buf3, n3 + n2 < # buf, n3 < # buf, m2 < # avol1, n2 < EB_PAGE_SIZE, # buf0 < LEB_SIZE, (n3 + # buf0) + n2 < LEB_SIZE, n3 < n0 + # buf, n6 < n5 + n1, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), min(n1, n2) ≤ n6, min(n1, n2) ≤ EB_PAGE_SIZE, n1 + n3 ≤ # buf + n0 ⊦ subarray(subarray(buf + mkempbuf(n0), 0, n1 + n3) + subarray(buf3, n1 + n3, n5), n3 + min(n1, n2), n4)[n7] = (n6 < n1 ⊃ (buf + mkempbuf(n0))[n6 + n3];subarray(buf3, n1 + n3, n5)[n6 - n1]), n4 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [min(n1, n2), n6, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: min(n1, n2), n6, n