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Proof step 199 from proof refine-read-buf (previous step)

# buf3 = n5 + n1, # avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + # buf4, avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf4), subarray(buf2, 0, n2 + n3) = subarray(buf4, m6, n2 + n3), n3 + m6 < LEB_SIZE, (n3 + m6) + n2 < LEB_SIZE, n3 < EB_PAGE_SIZE, m2 < # avol1, n2 + n3 < EB_PAGE_SIZE, n3 + m6 < # buf4, m6 < LEB_SIZE, m6 + 1 < # buf4, m6 + 1 < LEB_SIZE, m6 < # buf4, (n3 + m6) + n2 < # buf4, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), (n3 + m6) + n1 ≤ LEB_SIZE, n3 + min(n1, n2) ≤ EB_PAGE_SIZE, # buf4 ≤ LEB_SIZE, min(n1, n2) ≤ n1 + n5 ⊦ subarray(buf2, n3, min(n1, n2)) + subarray(subarray(buf4 + mkempbuf(n0), n3 + m6, n1) + subarray(buf3, n1, n5), min(n1, n2), n4) = subarray(buf4 + mkempbuf(n0), n3 + m6, n1) + subarray(buf3, n1, n5), EB_PAGE_SIZE = 1, n3 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 200:
⊦ m < n ↔ (∃ m0. m + m0 = n ∧ m0 ≠ 0)
Proof step 201:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf3 = n5 + n1, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + # buf4, avol1[m2] = mapped(buf4), avol0[m2] = mapped(buf4), subarray(buf2, 0, n2 + n3) = subarray(buf4, m6, n2 + n3), (n3 + m6) + n2 < # buf4, m6 + 1 < LEB_SIZE, m6 + 1 < # buf4, m6 < LEB_SIZE, n3 + m6 < # buf4, n2 + n3 < EB_PAGE_SIZE, m2 < # avol1, n3 < EB_PAGE_SIZE, (n3 + m6) + n2 < LEB_SIZE, n3 + m6 < LEB_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), min(n1, n2) ≤ n1 + n5, # buf4 ≤ LEB_SIZE, n3 + min(n1, n2) ≤ EB_PAGE_SIZE, (n3 + m6) + n1 ≤ LEB_SIZE, ∃ m0. m6 + m0 = # buf4 ∧ m0 ≠ 0 ⊦ subarray(buf2, n3, min(n1, n2)) + subarray(subarray(buf4 + mkempbuf(n0), n3 + m6, n1) + subarray(buf3, n1, n5), min(n1, n2), n4) = subarray(buf4 + mkempbuf(n0), n3 + m6, n1) + subarray(buf3, n1, n5), EB_PAGE_SIZE = 1, n3 = 0

Rule argument

spec: nat-basic name: addex seq: ⊦ m < n ↔ (∃ m0. m + m0 = n ∧ m0 ≠ 0) subst: [n, m] → [# buf4, m6] flags: <all paths>

Additional information

Used terms: # buf4, m6