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Proof step 102 from proof refine-read-buf (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 103:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf + n4 + n2 = # buf3, n1 + n5 = n4 + n2, LEB_SIZE = n3 + n2 + # buf0 + # buf, avol1[m2] = mapped((buf0 + buf) + subarray(buf2, 0, n2)), avol0[m2] = mapped(buf0 + buf), n0 < n4, m2 < # avol1, n2 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf0 + # buf, EB_PAGE_SIZE), # buf ≤ # buf3, n1 ≤ n2 + n3, # buf0 ≤ LEB_SIZE, n2 ≤ n1 ⊦ (mkempbuf(n1) + subarray(buf3, n1 + # buf, n5))[n2 + n0] = (n0 + n2 < n1 ⊃ (subarray(buf2, 0, n2) + mkempbuf(n3))[n0 + n2];subarray(buf3, n1 + # buf, n5)[n0 + n2 - n1])

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ m < n → n ≠ 0; (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% ⊦ m ≤ m + n; (s)