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Proof step 145 from proof refine-read-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, m6 + n5 + n1 = m0 + # buf3, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + # buf4, avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf4), subarray(buf2, 0, n2) = subarray(buf4, m6, n2), m6 + n2 < LEB_SIZE, m6 + n2 < # buf4, m6 < # buf4, m2 < # avol1, n2 < EB_PAGE_SIZE, m0 < # buf4, m0 < LEB_SIZE, m6 < LEB_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), n1 + m6 ≤ LEB_SIZE, min(n1, n2) ≤ EB_PAGE_SIZE, m6 ≤ # buf3 + m0, # buf4 ≤ LEB_SIZE, m0 ≤ m6 + n2, min(n1, n2) ≤ n1 + n5, m0 ≤ m6 ⊦ subarray(buf4, m0, m6 - m0) + subarray(buf2, 0, min(n1, n2)) + subarray(subarray(buf4 + mkempbuf(n0), m0, n1 + (m6 - m0)) + subarray(buf3, n1 + (m6 - m0), n5), (m6 - m0) + min(n1, n2), n4) = subarray(buf4 + mkempbuf(n0), m0, n1 + (m6 - m0)) + subarray(buf3, n1 + (m6 - m0), n5)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 146:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n1 + n5 = n4 + min(n1, n2), m6 + n5 + n1 = m0 + # buf3, LEB_SIZE = n0 + # buf4, avol1[m2] = mapped(buf4), avol0[m2] = mapped(buf4), m6 = n3 + m0, subarray(buf2, 0, n2) = subarray(buf4, m6, n2), m6 < LEB_SIZE, m0 < LEB_SIZE, m0 < # buf4, n2 < EB_PAGE_SIZE, m2 < # avol1, m6 < # buf4, m6 + n2 < # buf4, m6 + n2 < LEB_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m0 ≤ m6, min(n1, n2) ≤ n1 + n5, m0 ≤ m6 + n2, # buf4 ≤ LEB_SIZE, m6 ≤ # buf3 + m0, min(n1, n2) ≤ EB_PAGE_SIZE, n1 + m6 ≤ LEB_SIZE ⊦ subarray(buf4, m0, n3) + subarray(buf2, 0, min(n1, n2)) + subarray(subarray(buf4 + mkempbuf(n0), m0, n1 + n3) + subarray(buf3, n1 + n3, n5), n3 + min(n1, n2), n4) = subarray(buf4 + mkempbuf(n0), m0, n1 + n3) + subarray(buf3, n1 + n3, n5)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m0, m6, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m0, m6, n