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Proof step 182 from proof refine-read-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, min(n1, n2) + n4 = n1 + n5, n3 + n5 + n1 = # buf3, LEB_SIZE = n0 + # buf0 + # buf, avol0[m2] = mapped(buf0 + buf), avol1[m2] = mapped(buf0 + buf), n6 = n7 + min(n1, n2), subarray(buf2, 0, n2) = subarray(buf, n3, n2), min(n1, n2) < n1 + n5, n6 < n1 + n5, n3 < # buf3, n3 + n2 < # buf, n3 < # buf, m2 < # avol1, n2 < EB_PAGE_SIZE, # buf0 < LEB_SIZE, (n3 + # buf0) + n2 < LEB_SIZE, n3 < n0 + # buf, n6 < n5 + n1, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), min(n1, n2) ≤ n6, min(n1, n2) ≤ EB_PAGE_SIZE, n1 + n3 ≤ # buf + n0 ⊦ subarray(subarray(buf + mkempbuf(n0), 0, n1 + n3) + subarray(buf3, n1 + n3, n5), n3 + min(n1, n2), n4)[n7] = (n6 < n1 ⊃ (buf + mkempbuf(n0))[n6 + n3];subarray(buf3, n1 + n3, n5)[n6 - n1]), n4 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 183:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n3 + n5 + n1 = # buf3, min(n1, n2) + n4 = n1 + n5, LEB_SIZE = n0 + # buf0 + # buf, avol1[m2] = mapped(buf0 + buf), avol0[m2] = mapped(buf0 + buf), subarray(buf2, 0, n2) = subarray(buf, n3, n2), n7 < n4, n3 < n0 + # buf, (n3 + # buf0) + n2 < LEB_SIZE, # buf0 < LEB_SIZE, n2 < EB_PAGE_SIZE, m2 < # avol1, n3 < # buf, n3 + n2 < # buf, n3 < # buf3, min(n1, n2) < n1 + n5, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), n1 + n3 ≤ # buf + n0, min(n1, n2) ≤ EB_PAGE_SIZE ⊦ (subarray(buf + mkempbuf(n0), 0, n1 + n3) + subarray(buf3, n1 + n3, n5))[(n3 + min(n1, n2)) + n7] = (n7 + min(n1, n2) < n1 ⊃ (buf + mkempbuf(n0))[(n7 + min(n1, n2)) + n3];subarray(buf3, n1 + n3, n5)[n7 + min(n1, n2) - n1])

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)