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Proof step 43 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, LEB_SIZE = n0 + # buf4, avol1[m2] = mapped(buf1), avol0[m2] = mapped(buf4), n2 + (m0 ≤ m6 ⊃ 0;m0 - m6) < EB_PAGE_SIZE, m2 < # avol1, (m0 ≤ m6 ⊃ 0;m0 - m6) < EB_PAGE_SIZE, abs(avol1, buffered(m2), mkwbuf(buf2, m6, n2 + (m0 ≤ m6 ⊃ 0;m0 - m6)), avol0, rofs), awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m6 ≤ # buf1 + (LEB_SIZE - # buf1), # buf1 ≤ LEB_SIZE, m6 ≤ LEB_SIZE, (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, (m0 ≤ m6 ⊃ 0;m0 - m6) + min(n1, n2) ≤ EB_PAGE_SIZE, (m0 ≤ m6 ⊃ m6 - m0;0) + min(n1, n2) ≤ # buf3, m0 ≤ m6 + n2 + (m0 ≤ m6 ⊃ 0;m0 - m6), m6 ≤ m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0), n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ LEB_SIZE, # buf4 ≤ LEB_SIZE, m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf1 + (LEB_SIZE - # buf1), ¬ m0 ≤ m6 → m6 ≤ m0, rofs → m6 ≤ # buf4, ¬ rofs → # buf4 = m6 ⊦ copy(buf2, (m0 ≤ m6 ⊃ 0;m0 - m6), copy(buf4 + mkempbuf(n0), m0, buf3, 0, n1 + (m0 ≤ m6 ⊃ m6 - m0;0)), (m0 ≤ m6 ⊃ m6 - m0;0), min(n1, n2)) = copy(buf1 + mkempbuf(LEB_SIZE - # buf1), m0, buf3, 0, n1 + (m0 ≤ m6 ⊃ m6 - m0;0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 44:
# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, LEB_SIZE = n0 + # buf4, LEB_SIZE = n3 + # buf1, avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf1), (m0 ≤ m6 ⊃ 0;m0 - m6) < EB_PAGE_SIZE, m2 < # avol1, n2 + (m0 ≤ m6 ⊃ 0;m0 - m6) < EB_PAGE_SIZE, abs(avol1, buffered(m2), mkwbuf(buf2, m6, n2 + (m0 ≤ m6 ⊃ 0;m0 - m6)), avol0, rofs), awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf1 + n3, # buf4 ≤ LEB_SIZE, m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ LEB_SIZE, n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, m6 ≤ m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0), m0 ≤ m6 + n2 + (m0 ≤ m6 ⊃ 0;m0 - m6), (m0 ≤ m6 ⊃ m6 - m0;0) + min(n1, n2) ≤ # buf3, (m0 ≤ m6 ⊃ 0;m0 - m6) + min(n1, n2) ≤ EB_PAGE_SIZE, (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, m6 ≤ LEB_SIZE, # buf1 ≤ LEB_SIZE, m6 ≤ # buf1 + n3, ¬ rofs → # buf4 = m6, rofs → m6 ≤ # buf4, ¬ m0 ≤ m6 → m6 ≤ m0 ⊦ copy(buf2, (m0 ≤ m6 ⊃ 0;m0 - m6), copy(buf4 + mkempbuf(n0), m0, buf3, 0, n1 + (m0 ≤ m6 ⊃ m6 - m0;0)), (m0 ≤ m6 ⊃ m6 - m0;0), min(n1, n2)) = copy(buf1 + mkempbuf(n3), m0, buf3, 0, n1 + (m0 ≤ m6 ⊃ m6 - m0;0))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [# buf1, LEB_SIZE, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf1, LEB_SIZE, n