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Proof step 74 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol1[m4] = mapped(buf2 + subarray(buf1, 0, m2)), avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, m4 < # avol1, m2 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n + m2, EB_PAGE_SIZE), (# buf2 + m2) + n3 ≤ LEB_SIZE, n + (m2 + n3) % EB_PAGE_SIZE ≤ # buf3, # buf2 + n + m2 ≤ LEB_SIZE, n ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, 0 + m2 ≤ # buf1, 0 + m2 ≤ # mkbuf(n + m2) ⊦ subarray(buf1, 0, m2) + subarray(buf3, 0, n3) = copy(buf3, 0, subarray(mkbuf(n + m2), 0, 0) + subarray(buf1, 0, m2) + subarray(mkbuf(n + m2), 0 + m2, # mkbuf(n + m2) - 0 - m2), m2, n) + subarray(buf3, n, (m2 + n3) % EB_PAGE_SIZE), n + m2 = 0, n3 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol1[m4] = mapped(buf2 + subarray(buf1, 0, m2)), avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, m4 < # avol1, m2 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n + m2, EB_PAGE_SIZE), (# buf2 + m2) + n3 ≤ LEB_SIZE, n + (m2 + n3) % EB_PAGE_SIZE ≤ # buf3, # buf2 + n + m2 ≤ LEB_SIZE, n ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3 ⊦ n + m2 = 0, n3 = 0, subarray(buf3, 0, n3) = copy(buf3, 0, subarray(mkbuf(n + m2), m2, n), 0, n) + subarray(buf3, n, (m2 + n3) % EB_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)% ⊦ m ≤ m + n; (s)% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)% ⊦ m - m = 0; (s)%# buf ≤ m0 ⊦ copy(buf0, m, buf + buf1, m0, m1) = buf + copy(buf0, m, buf1, m0 - # buf, m1); (s)% ⊦ ¬ n < n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mkbuf(0) + buf = buf; (s)% ⊦ m + n - m = n; (s)% ⊦ m - 0 = m; (s)% ⊦ # mkbuf(n) = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)