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Proof step 196 from proof refine-read-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, # buf3 = n5 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0), n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + # buf4, avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf4), subarray(buf2, 0, n2 + (m0 ≤ m6 ⊃ 0;m0 - m6)) = subarray(buf4, m6, n2 + (m0 ≤ m6 ⊃ 0;m0 - m6)), m0 < LEB_SIZE, m6 < LEB_SIZE, m6 + n2 + (m0 ≤ m6 ⊃ 0;m0 - m6) < # buf4, m6 < # buf4, (m0 ≤ m6 ⊃ 0;m0 - m6) < EB_PAGE_SIZE, m2 < # avol1, n2 + (m0 ≤ m6 ⊃ 0;m0 - m6) < EB_PAGE_SIZE, m0 < # buf4, m6 + n2 + (m0 ≤ m6 ⊃ 0;m0 - m6) < LEB_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ LEB_SIZE, (m0 ≤ m6 ⊃ 0;m0 - m6) + min(n1, n2) ≤ EB_PAGE_SIZE, (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, # buf4 ≤ LEB_SIZE, m6 ≤ m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0), m0 ≤ m6 + n2 + (m0 ≤ m6 ⊃ 0;m0 - m6), min(n1, n2) ≤ n1 + n5, ¬ m0 ≤ m6 → m6 ≤ m0 ⊦ subarray(buf4, m0, (m0 ≤ m6 ⊃ m6 - m0;0)) + subarray(buf2, (m0 ≤ m6 ⊃ 0;m0 - m6), min(n1, n2)) + subarray (subarray(buf4 + mkempbuf(n0), m0, n1 + (m0 ≤ m6 ⊃ m6 - m0;0)) + subarray(buf3, n1 + (m0 ≤ m6 ⊃ m6 - m0;0), n5), (m0 ≤ m6 ⊃ m6 - m0;0) + min(n1, n2), n4) = subarray(buf4 + mkempbuf(n0), m0, n1 + (m0 ≤ m6 ⊃ m6 - m0;0)) + subarray(buf3, n1 + (m0 ≤ m6 ⊃ m6 - m0;0), n5), m0 ≤ m6

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 197:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf3 = n5 + n1, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + # buf4, avol1[m2] = mapped(buf4), avol0[m2] = mapped(buf4), subarray(buf2, 0, n2 + (m0 - m6)) = subarray(buf4, m6, n2 + (m0 - m6)), m6 + 1 < LEB_SIZE, m6 + 1 < # buf4, m0 + n2 < LEB_SIZE, m6 < m0, m6 < LEB_SIZE, m0 < LEB_SIZE, m0 < # buf4, n2 + (m0 - m6) < EB_PAGE_SIZE, m2 < # avol1, m0 < EB_PAGE_SIZE + m6, m0 + n2 < # buf4, m6 < # buf4, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), min(n1, n2) ≤ n1 + n5, m6 ≤ m0 + n1, # buf4 ≤ LEB_SIZE, m0 + min(n1, n2) ≤ EB_PAGE_SIZE + m6, m0 + n1 ≤ LEB_SIZE ⊦ subarray(buf2, m0 - m6, min(n1, n2)) + subarray(subarray(buf4 + mkempbuf(n0), m0, n1) + subarray(buf3, n1, n5), min(n1, n2), n4) = subarray(buf4 + mkempbuf(n0), m0, n1) + subarray(buf3, n1, n5), EB_PAGE_SIZE = 1

Rule argument

Additional information

Used simplifier rules: ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m + n < m0 → m + n < m0 + n0; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ EB_PAGE_SIZE + n = 0 ↔ false; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m ≤ m + n; (s)%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ n < m → (m - n) + n = m; (s)% ⊦ m < n → m ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ 0 ≤ m; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mkbuf(0) + buf = buf; (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (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)