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Proof step 223 from proof refine-read-buf (previous step)

# subarray(buf2, 0, n2 + n3) = # subarray(buf, 0, n2 + n3), # buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf3 = n5 + n1, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + # buf0 + # buf, avol1[m2] = mapped(buf0 + buf), avol0[m2] = mapped(buf0 + buf), n < min(n1, n2), n < n5 + n1, n3 + n2 < # buf, # buf0 + 1 < LEB_SIZE, # buf0 < LEB_SIZE, n3 < # buf, n2 + n3 < EB_PAGE_SIZE, m2 < # avol1, n3 < EB_PAGE_SIZE, (n3 + # buf0) + n2 < LEB_SIZE, n3 < n0 + # buf, n < n1 + n5, n3 + n < # buf, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf0, EB_PAGE_SIZE), min(n1, n2) ≤ n1 + n5, n3 + min(n1, n2) ≤ EB_PAGE_SIZE, n3 + n1 ≤ # buf + n0, ∀ n. n < # subarray(buf2, 0, n2 + n3) → subarray(buf2, 0, n2 + n3)[n] = subarray(buf, 0, n2 + n3)[n] ⊦ # buf = 1, EB_PAGE_SIZE = 1, buf2[n3 + n] = buf[n3 + n], n3 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 224:
# buf3 = n5 + n1, # avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + # buf0 + # buf, avol0[m2] = mapped(buf0 + buf), avol1[m2] = mapped(buf0 + buf), n3 + n < # buf, n < n1 + n5, n3 < n0 + # buf, (n3 + # buf0) + n2 < LEB_SIZE, n3 < EB_PAGE_SIZE, m2 < # avol1, n2 + n3 < EB_PAGE_SIZE, n3 < # buf, # buf0 < LEB_SIZE, # buf0 + 1 < LEB_SIZE, n3 + n2 < # buf, n < n5 + n1, n < min(n1, n2), awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf0, EB_PAGE_SIZE), n3 + n1 ≤ # buf + n0, n3 + min(n1, n2) ≤ EB_PAGE_SIZE, min(n1, n2) ≤ n1 + n5, ∀ n6. n6 < n2 + n3 → buf2[n6] = buf[n6] ⊦ # buf = 1, EB_PAGE_SIZE = 1, buf2[n3 + n] = buf[n3 + n], n3 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ # subarray(buf, m, n) = n; (s)