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Proof step 147 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n3 + n5 + n1 = # buf3, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + # buf4, avol1[m2] = mapped(buf4), avol0[m2] = mapped(buf4), subarray(buf2, 0, n2) = subarray(buf4, n3 + m0, n2), n3 + m0 < LEB_SIZE, (n3 + m0) + n2 < LEB_SIZE, m0 < LEB_SIZE, m0 < # buf4, n2 < EB_PAGE_SIZE, m2 < # avol1, n3 + m0 < # buf4, (n3 + m0) + n2 < # buf4, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + m0, EB_PAGE_SIZE), n3 ≤ # buf3, min(n1, n2) ≤ EB_PAGE_SIZE, n1 + n3 + m0 ≤ LEB_SIZE, min(n1, n2) ≤ n1 + n5, # buf4 ≤ LEB_SIZE ⊦ subarray(buf4, m0, n3) + subarray(buf2, 0, min(n1, n2)) + subarray(subarray(buf4 + mkempbuf(n0), m0, n1 + n3) + subarray(buf3, n1 + n3, n5), n3 + min(n1, n2), n4) = subarray(buf4 + mkempbuf(n0), m0, n1 + n3) + subarray(buf3, n1 + n3, n5)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 148:
⊦ m < n ↔ (∃ m0. m + m0 = n ∧ m0 ≠ 0)
Proof step 149:
# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, n1 + n5 = n4 + min(n1, n2), n3 + n5 + n1 = # buf3, LEB_SIZE = n0 + # buf4, avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf4), subarray(buf2, 0, n2) = subarray(buf4, n3 + m0, n2), (n3 + m0) + n2 < # buf4, n3 + m0 < # buf4, m2 < # avol1, n2 < EB_PAGE_SIZE, m0 < LEB_SIZE, (n3 + m0) + n2 < LEB_SIZE, n3 + m0 < LEB_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + m0, EB_PAGE_SIZE), # buf4 ≤ LEB_SIZE, min(n1, n2) ≤ n1 + n5, n1 + n3 + m0 ≤ LEB_SIZE, min(n1, n2) ≤ EB_PAGE_SIZE, n3 ≤ # buf3, ∃ m1. m0 + m1 = # buf4 ∧ m1 ≠ 0 ⊦ subarray(buf4, m0, n3) + subarray(buf2, 0, min(n1, n2)) + subarray(subarray(buf4 + mkempbuf(n0), m0, n1 + n3) + subarray(buf3, n1 + n3, n5), n3 + min(n1, n2), n4) = subarray(buf4 + mkempbuf(n0), m0, n1 + n3) + subarray(buf3, n1 + n3, n5)

Rule argument

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

Additional information

Used terms: # buf4, m0