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Proof step 101 from proof refine-read-buf (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 102:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf + n4 + n2 = # buf3, n1 + n5 = n4 + n2, LEB_SIZE = n3 + n2 + # buf0 + # buf, avol1[m2] = mapped((buf0 + buf) + subarray(buf2, 0, n2)), avol0[m2] = mapped(buf0 + buf), n = n0 + n2, m2 < # avol1, n2 < EB_PAGE_SIZE, n < n2 + n4, n < n4 + n2, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf0 + # buf, EB_PAGE_SIZE), # buf ≤ # buf3, n1 ≤ n2 + n3, # buf0 ≤ LEB_SIZE, n2 ≤ n1, n2 ≤ n ⊦ subarray(mkempbuf(n1) + subarray(buf3, n1 + # buf, n5), n2, n4)[n0] = (n < n1 ⊃ (subarray(buf2, 0, n2) + mkempbuf(n3))[n];subarray(buf3, n1 + # buf, n5)[n - n1]), n4 = 0

Rule argument

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

Additional information

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