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Proof step 144 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, ¬ 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 145:
# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, m6 + n5 + n1 = m0 + # buf3, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + # buf4, avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf4), subarray(buf2, 0, n2) = subarray(buf4, m6, n2), m6 + n2 < LEB_SIZE, m6 + n2 < # buf4, m6 < # buf4, m2 < # avol1, n2 < EB_PAGE_SIZE, m0 < # buf4, m0 < LEB_SIZE, m6 < LEB_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), n1 + m6 ≤ LEB_SIZE, min(n1, n2) ≤ EB_PAGE_SIZE, m6 ≤ # buf3 + m0, # buf4 ≤ LEB_SIZE, m0 ≤ m6 + n2, min(n1, n2) ≤ n1 + n5, m0 ≤ m6 ⊦ subarray(buf4, m0, m6 - m0) + subarray(buf2, 0, min(n1, n2)) + subarray(subarray(buf4 + mkempbuf(n0), m0, n1 + (m6 - m0)) + subarray(buf3, n1 + (m6 - m0), n5), (m6 - m0) + min(n1, n2), n4) = subarray(buf4 + mkempbuf(n0), m0, n1 + (m6 - m0)) + subarray(buf3, n1 + (m6 - m0), n5)

Rule argument

Additional information

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