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Proof step 287 from proof refine-read-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, LEB_SIZE = n0 + # buf, avol0[m2] = mapped(buf), avol1[m2] = mapped(buf1), m2 < # avol1, m4 < EB_PAGE_SIZE, abs(avol1, buffered(m2), mkwbuf(buf2, m6, m4), avol0, rofs), awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), (m0 ≤ m6 ⊃ m6 - m0;0) ≤ n, m6 ≤ # buf, # buf ≤ LEB_SIZE, m0 + n ≤ LEB_SIZE, n ≤ # buf3, m6 ≤ m0 + n, m0 ≤ m6 + m4, m6 ≤ LEB_SIZE, (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, ¬ rofs → # buf = m6, ¬ m0 ≤ m6 → m6 ≤ m0 ⊦ (m0 ≤ m6 ⊃ 0;m0 - m6) + min(n - (m0 ≤ m6 ⊃ m6 - m0;0), m4 - (m0 ≤ m6 ⊃ 0;m0 - m6)) ≤ EB_PAGE_SIZE ∧ (m0 ≤ m6 ⊃ m6 - m0;0) + min(n - (m0 ≤ m6 ⊃ m6 - m0;0), m4 - (m0 ≤ m6 ⊃ 0;m0 - m6)) ≤ # buf3 ∧ (m0 ≤ m6 ⊃ 0;m0 - m6) ≤ m4

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 288:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, LEB_SIZE = n0 + # buf, avol1[m2] = mapped(buf1), avol0[m2] = mapped(buf), n = n1 + (m0 ≤ m6 ⊃ m6 - m0;0), m4 < EB_PAGE_SIZE, m2 < # avol1, abs(avol1, buffered(m2), mkwbuf(buf2, m6, m4), avol0, rofs), awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, m6 ≤ LEB_SIZE, m0 ≤ m6 + m4, m6 ≤ m0 + n, n ≤ # buf3, m0 + n ≤ LEB_SIZE, # buf ≤ LEB_SIZE, m6 ≤ # buf, (m0 ≤ m6 ⊃ m6 - m0;0) ≤ n, ¬ m0 ≤ m6 → m6 ≤ m0, ¬ rofs → # buf = m6 ⊦ (m0 ≤ m6 ⊃ 0;m0 - m6) + min(n1, m4 - (m0 ≤ m6 ⊃ 0;m0 - m6)) ≤ EB_PAGE_SIZE ∧ (m0 ≤ m6 ⊃ m6 - m0;0) + min(n1, m4 - (m0 ≤ m6 ⊃ 0;m0 - m6)) ≤ # buf3 ∧ (m0 ≤ m6 ⊃ 0;m0 - m6) ≤ m4

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [(m0 ≤ m6 ⊃ m6 - m0;0), n, n1]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: (m0 ≤ m6 ⊃ m6 - m0;0), n, n1