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Proof step 273 from proof refine-read-buf (previous step)

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

User applied rule apply lemma

And obtained the following new goals

Proof step 274:
⊦ n ≤ # buf → (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = n)
Proof step 275:
# buf3 = n5 + n1, # buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n1 + n5 = n4 + min(n1, n2), (n0 + # buf4) + n3 + n2 = LEB_SIZE, avol1[m2] = mapped(buf4 + subarray(buf2, 0, n2 + n0)), avol0[m2] = mapped(buf4), n2 + n0 < EB_PAGE_SIZE, m2 < # avol1, n0 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf4, EB_PAGE_SIZE), min(n1, n2) ≤ n1 + n5, # buf4 ≤ LEB_SIZE, n0 + min(n1, n2) ≤ EB_PAGE_SIZE, n1 ≤ n2 + n3, n0 ≤ # buf2 → (∃ buf0, buf1. buf2 = buf0 + buf1 ∧ # buf0 = n0) ⊦ subarray(buf2, n0, min(n1, n2)) + subarray(mkempbuf(n1) + subarray(buf3, n1, n5), min(n1, n2), n4) = subarray(subarray(buf2, 0, n2 + n0) + mkempbuf(n3), n0, n1) + subarray(buf3, n1, n5), EB_PAGE_SIZE = 1, n0 = 0

Rule argument

spec: array-splice, inst: buffer name: array-split1 seq: ⊦ n ≤ # buf → (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = n) subst: [n, buf] → [n0, buf2]

Additional information

Used terms: n0, buf2