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Proof step 70 from proof refine-read-buf (previous step)

# buf3 = n5 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0), # buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n3 + # buf1, LEB_SIZE = n0 + # buf4, avol1[m2] = mapped(buf1), avol0[m2] = mapped(buf4), buf1 = buf4 + subarray(buf2, 0, n2 + (m0 ≤ # buf4 ⊃ 0;m0 - # buf4)), m6 = # buf4, n2 + (m0 ≤ m6 ⊃ 0;m0 - m6) < EB_PAGE_SIZE, m2 < # avol1, (m0 ≤ m6 ⊃ 0;m0 - m6) < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m6 ≤ # buf4, min(n1, n2) ≤ n1 + n5, m0 ≤ m6 + n2 + (m0 ≤ m6 ⊃ 0;m0 - m6), m6 ≤ m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0), # buf4 ≤ LEB_SIZE, # buf1 ≤ LEB_SIZE, m6 ≤ LEB_SIZE, (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, (m0 ≤ m6 ⊃ 0;m0 - m6) + min(n1, n2) ≤ EB_PAGE_SIZE, m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ LEB_SIZE, ¬ m0 ≤ m6 → m6 ≤ m0 ⊦ subarray(buf4 + mkempbuf(n0), 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(buf1 + mkempbuf(n3), 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 71:
# buf3 = n5 + n1 + (m0 ≤ # buf4 ⊃ # buf4 - m0;0), # buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = (n3 + n2 + (m0 ≤ # buf4 ⊃ 0;m0 - # buf4)) + # buf4, avol1[m2] = mapped(buf4 + subarray(buf2, 0, n2 + (m0 ≤ # buf4 ⊃ 0;m0 - # buf4))), avol0[m2] = mapped(buf4), n2 + (m0 ≤ # buf4 ⊃ 0;m0 - # buf4) < EB_PAGE_SIZE, m2 < # avol1, (m0 ≤ # buf4 ⊃ 0;m0 - # buf4) < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf4, EB_PAGE_SIZE), min(n1, n2) ≤ n1 + n5, m0 ≤ # buf4 + n2 + (m0 ≤ # buf4 ⊃ 0;m0 - # buf4), # buf4 ≤ m0 + n1 + (m0 ≤ # buf4 ⊃ # buf4 - m0;0), # buf4 ≤ LEB_SIZE, (m0 ≤ # buf4 ⊃ # buf4 - m0;0) ≤ # buf3, (m0 ≤ # buf4 ⊃ 0;m0 - # buf4) + min(n1, n2) ≤ EB_PAGE_SIZE, m0 + n1 + (m0 ≤ # buf4 ⊃ # buf4 - m0;0) ≤ LEB_SIZE, ¬ m0 ≤ # buf4 → # buf4 ≤ m0 ⊦ subarray(buf4 + mkempbuf(n3 + n2 + (m0 ≤ # buf4 ⊃ 0;m0 - # buf4)), m0, (m0 ≤ # buf4 ⊃ # buf4 - m0;0)) + subarray(buf2, (m0 ≤ # buf4 ⊃ 0;m0 - # buf4), min(n1, n2)) + subarray ( subarray(buf4 + mkempbuf(n3 + n2 + (m0 ≤ # buf4 ⊃ 0;m0 - # buf4)), m0, n1 + (m0 ≤ # buf4 ⊃ # buf4 - m0;0)) + subarray(buf3, n1 + (m0 ≤ # buf4 ⊃ # buf4 - m0;0), n5), (m0 ≤ # buf4 ⊃ # buf4 - m0;0) + min(n1, n2), n4) = subarray((buf4 + subarray(buf2, 0, n2 + (m0 ≤ # buf4 ⊃ 0;m0 - # buf4))) + mkempbuf(n3), m0, n1 + (m0 ≤ # buf4 ⊃ # buf4 - m0;0)) + subarray(buf3, n1 + (m0 ≤ # buf4 ⊃ # buf4 - m0;0), n5)

Rule argument

Additional information

Used simplifier rules: nat0: ⊦ n0 = n1 + n → (n1 + m ≤ n0 ↔ m ≤ n);%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ m ≤ m + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)