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Proof step 114 from proof refine-read-buf (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 115:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf3 = n5 + n1, (n0 + # buf4) + n3 + n2 = LEB_SIZE, avol1[m2] = mapped(buf4 + subarray(buf2, 0, n2 + n0)), avol0[m2] = mapped(buf4), n0 < EB_PAGE_SIZE, n2 + n0 < EB_PAGE_SIZE, m2 < # avol1, n1 < n2, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf4, EB_PAGE_SIZE), n0 + n1 ≤ EB_PAGE_SIZE, n1 ≤ n2 + n3, # buf4 ≤ LEB_SIZE ⊦ EB_PAGE_SIZE = 1, n0 = 0, subarray(buf2, n0, n1) = subarray(subarray(buf2, 0, n2 + n0), n0, n1)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ buf + buf0 = buf1 + buf0 ↔ buf = buf1; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ m < n → m ≤ n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m - m = 0; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m ≤ m; (s)% ⊦ # mkempbuf(n) = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)