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Proof step 29 from proof inv-read-buf (previous step)

# lpt = # avol, # buf1 = EB_PAGE_SIZE, LEB_SIZE = n0 + # buf2, avol[m3] = mapped(buf2), EB_PAGE_SIZE < (m0 ≤ m5 ⊃ 0;m0 - m5) + min(n1, m4 - (m0 ≤ m5 ⊃ 0;m0 - m5)), m3 < # avol, ebm-vol-inv(avol), wbuf-cons(mkwbuf(buf1, m5, m4), mapped(buf2), rofs), (m0 ≤ m5 ⊃ m5 - m0;0) + min(n1, m4 - (m0 ≤ m5 ⊃ 0;m0 - m5)) ≤ # buf, # buf2 ≤ LEB_SIZE, n1 + (m0 ≤ m5 ⊃ m5 - m0;0) ≤ # buf, m0 + n1 + (m0 ≤ m5 ⊃ m5 - m0;0) ≤ LEB_SIZE, m5 ≤ m0 + n1 + (m0 ≤ m5 ⊃ m5 - m0;0), m0 ≤ m5 + m4, m5 ≤ LEB_SIZE, (m0 ≤ m5 ⊃ m5 - m0;0) ≤ # buf, (m0 ≤ m5 ⊃ 0;m0 - m5) ≤ m4, ¬ m0 ≤ m5 → m5 ≤ m0 ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
# buf1 = EB_PAGE_SIZE, # lpt = # avol, LEB_SIZE = n0 + # buf2, avol[m3] = mapped(buf2), m4 = n2 + (m0 ≤ m5 ⊃ 0;m0 - m5), m3 < # avol, EB_PAGE_SIZE < (m0 ≤ m5 ⊃ 0;m0 - m5) + min(n1, n2), ebm-vol-inv(avol), wbuf-cons(mkwbuf(buf1, m5, m4), mapped(buf2), rofs), (m0 ≤ m5 ⊃ 0;m0 - m5) ≤ m4, (m0 ≤ m5 ⊃ m5 - m0;0) ≤ # buf, m5 ≤ LEB_SIZE, m0 ≤ m5 + m4, m5 ≤ m0 + n1 + (m0 ≤ m5 ⊃ m5 - m0;0), m0 + n1 + (m0 ≤ m5 ⊃ m5 - m0;0) ≤ LEB_SIZE, n1 + (m0 ≤ m5 ⊃ m5 - m0;0) ≤ # buf, # buf2 ≤ LEB_SIZE, (m0 ≤ m5 ⊃ m5 - m0;0) + min(n1, n2) ≤ # buf, ¬ m0 ≤ m5 → m5 ≤ m0 ⊦

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [(m0 ≤ m5 ⊃ 0;m0 - m5), m4, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: (m0 ≤ m5 ⊃ 0;m0 - m5), m4, n