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Proof step 278 from proof refine-read-buf (previous step)

# lpt0 = # avol1, # avol0 = # avol1, # buf3 = n5 + n1, # buf + # buf0 = EB_PAGE_SIZE, n1 + n5 = n4 + min(n1, n2), (# buf + # buf4) + n3 + n2 = LEB_SIZE, avol1[m2] = mapped(buf4 + buf + subarray(buf0, 0, n2)), avol0[m2] = mapped(buf4), # buf < EB_PAGE_SIZE, m2 < # avol1, n2 < # buf0, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf4, EB_PAGE_SIZE), min(n1, n2) ≤ # buf0, n1 ≤ n2 + n3, min(n1, n2) ≤ n1 + n5, # buf4 ≤ LEB_SIZE, # subarray(buf0, 0, n2) ≤ n1, n1 ≤ # subarray(buf0, 0, n2) + # mkempbuf(n3) ⊦ # buf = 0, subarray(buf0, 0, min(n1, n2)) + subarray(mkempbuf(n1) + subarray(buf3, n1, n5), min(n1, n2), n4) = (subarray(buf0, 0, n2) + subarray(mkempbuf(n3), 0, n1 - # subarray(buf0, 0, n2))) + subarray(buf3, n1, n5), EB_PAGE_SIZE = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 279:
# lpt0 = # avol1, # avol0 = # avol1, # buf3 = n4 + n2, n1 + n5 = n4 + n2, (# buf + # buf4) + n3 + n2 = LEB_SIZE, # buf + # buf0 = EB_PAGE_SIZE, avol1[m2] = mapped(buf4 + buf + subarray(buf0, 0, n2)), avol0[m2] = mapped(buf4), # buf < EB_PAGE_SIZE, m2 < # avol1, n2 < # buf0, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf4, EB_PAGE_SIZE), # buf4 ≤ LEB_SIZE, n2 ≤ n1, n1 ≤ n2 + n3 ⊦ # buf = 0, EB_PAGE_SIZE = 1, subarray(mkempbuf(n1) + subarray(buf3, n1, n5), n2, n4) = subarray(mkempbuf(n3), 0, n1 - n2) + subarray(buf3, n1, n5)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → m ≤ n; (s)% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)%min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ n0 ≤ n1 → min(n0, n1) = n0; (s)% ⊦ # mkempbuf(n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)