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Proof step 202 from proof refine-read-buf (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 203:
⊦ # buf = n0 + n1 ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = n0 ∧ # buf1 = n1)
Proof step 204:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf3 = n5 + n1, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + m6 + m, avol1[m2] = mapped(buf4), avol0[m2] = mapped(buf4), subarray(buf2, 0, n2 + n3) = subarray(buf4, m6, n2 + n3), n3 + n2 < m, m6 + 1 < LEB_SIZE, m6 < LEB_SIZE, n3 < m, 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, n3 + min(n1, n2) ≤ EB_PAGE_SIZE, n3 + n1 ≤ m + n0, ∃ buf0, buf1. buf4 = buf0 + buf1 ∧ # buf0 = m6 ∧ # buf1 = m ⊦ 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), n0 + m = 0, EB_PAGE_SIZE = 1, m = 1, n3 = 0

Rule argument

spec: array-splice, inst: buffer name: array-split-elim-size seq: ⊦ # buf = n0 + n1 ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = n0 ∧ # buf1 = n1) subst: [buf, n1, n0] → [buf4, m, m6] flags: <all paths>

Additional information

Used terms: buf4, m, m6