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Proof step 327 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, LEB_SIZE = n0 + # buf, LEB_SIZE = n1 + # buf1, avol0[n2] = mapped(buf), avol1[n2] = mapped(buf1), n2 < # avol1, m4 < EB_PAGE_SIZE, n3 < # buf3, n3 + m0 < # buf + # mkempbuf(n0), awbuf-inv(avol1, buffered(n2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m0 + n ≤ LEB_SIZE, # buf ≤ LEB_SIZE, n ≤ # buf3, # buf1 ≤ LEB_SIZE, rofs → m6 = # buf ∧ buf1 = buf + subarray(buf2, 0, m4) ∨ m6 < # buf ∧ m6 + m4 < # buf ∧ buf1 = buf ∧ subarray(buf2, 0, m4) = subarray(buf, m6, m4), ¬ rofs → buf1 = buf + subarray(buf2, 0, m4), rofs → m6 ≤ # buf, ¬ rofs → # buf = m6 ⊦ (n ≤ n3 ⊃ buf3[n3];(n3 + m0 < # buf ⊃ buf[n3 + m0];mkempbuf(n0)[n3 + m0 - # buf])) = (n ≤ n3 ⊃ buf3[n3];(buf1 + mkempbuf(n1))[n3 + m0]), m0 ≤ m6 + m4 ∧ m6 ≤ m0 + n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 328:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, LEB_SIZE = n0 + # buf, LEB_SIZE = n1 + # buf1, avol0[n2] = mapped(buf), avol1[n2] = mapped(buf1), n3 + m0 < LEB_SIZE, n2 < # avol1, m4 < EB_PAGE_SIZE, n3 < # buf3, awbuf-inv(avol1, buffered(n2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m0 + n ≤ LEB_SIZE, # buf ≤ LEB_SIZE, n ≤ # buf3, # buf1 ≤ LEB_SIZE, rofs → m6 = # buf ∧ buf1 = buf + subarray(buf2, 0, m4) ∨ m6 < # buf ∧ m6 + m4 < # buf ∧ buf1 = buf ∧ subarray(buf2, 0, m4) = subarray(buf, m6, m4), ¬ rofs → buf1 = buf + subarray(buf2, 0, m4), rofs → m6 ≤ # buf, ¬ rofs → # buf = m6 ⊦ (n ≤ n3 ⊃ buf3[n3];(n3 + m0 < # buf ⊃ buf[n3 + m0];mkempbuf(n0)[n3 + m0 - # buf])) = (n ≤ n3 ⊃ buf3[n3];(buf1 + mkempbuf(n1))[n3 + m0]), m0 ≤ m6 + m4 ∧ m6 ≤ m0 + n

Rule argument

Additional information

Used simplifier rules: ⊦ LEB_SIZE ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # mkempbuf(n) = n; (s)