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Proof step 174 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n3 + n5 + n1 = # buf3, min(n1, n2) + n4 = n1 + n5, LEB_SIZE = n0 + # buf0 + # buf, avol1[m2] = mapped(buf0 + buf), avol0[m2] = mapped(buf0 + buf), subarray(buf2, 0, n2) = subarray(buf, n3, n2), n6 < min(n1, n2), n6 < n5 + n1, n3 < n0 + # buf, (n3 + # buf0) + n2 < LEB_SIZE, # buf0 < LEB_SIZE, n2 < EB_PAGE_SIZE, m2 < # avol1, n3 < # buf, n3 + n2 < # buf, n3 < # buf3, n6 < n1 + n5, n6 < EB_PAGE_SIZE, n6 + n3 < # buf + n0, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), n1 + n3 ≤ # buf + n0, min(n1, n2) ≤ n1 + n5, min(n1, n2) ≤ EB_PAGE_SIZE ⊦ buf2[n6] = (n6 + n3 < # buf ⊃ buf[n6 + n3];mkempbuf(n0)[n6 + n3 - # buf])

User applied rule case distinction

And obtained the following new goals

Proof step 175:
# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, min(n1, n2) + n4 = n1 + n5, n3 + n5 + n1 = # buf3, LEB_SIZE = n0 + # buf0 + # buf, avol0[m2] = mapped(buf0 + buf), avol1[m2] = mapped(buf0 + buf), subarray(buf2, 0, n2) = subarray(buf, n3, n2), n6 + n3 < # buf + n0, n6 < EB_PAGE_SIZE, n6 < n1 + n5, n3 < # buf3, n3 + n2 < # buf, n3 < # buf, m2 < # avol1, n2 < EB_PAGE_SIZE, # buf0 < LEB_SIZE, (n3 + # buf0) + n2 < LEB_SIZE, n3 < n0 + # buf, n6 < n5 + n1, n6 < min(n1, n2), n6 + n3 < # buf, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), min(n1, n2) ≤ EB_PAGE_SIZE, min(n1, n2) ≤ n1 + n5, n1 + n3 ≤ # buf + n0 ⊦ buf2[n6] = buf[n6 + n3]

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < m + n ↔ n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]% ⊦ m +1 = m + 1; (s)% ⊦ ¬ m < min(n, m); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ # subarray(buf, m, n) = n; (s)