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Proof step 204 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf3 = n5 + n1, n1 + n5 = n4 + min(n1, n2), LEB_SIZE = n0 + m6 + m, avol1[m2] = mapped(buf4), avol0[m2] = mapped(buf4), subarray(buf2, 0, n2 + n3) = subarray(buf4, m6, n2 + n3), n3 + n2 < m, m6 + 1 < LEB_SIZE, m6 < LEB_SIZE, n3 < m, n2 + n3 < EB_PAGE_SIZE, m2 < # avol1, n3 < EB_PAGE_SIZE, (n3 + m6) + n2 < LEB_SIZE, n3 + m6 < LEB_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), min(n1, n2) ≤ n1 + n5, n3 + min(n1, n2) ≤ EB_PAGE_SIZE, n3 + n1 ≤ m + n0, ∃ buf0, buf1. buf4 = buf0 + buf1 ∧ # buf0 = m6 ∧ # buf1 = m ⊦ subarray(buf2, n3, min(n1, n2)) + subarray(subarray(buf4 + mkempbuf(n0), n3 + m6, n1) + subarray(buf3, n1, n5), min(n1, n2), n4) = subarray(buf4 + mkempbuf(n0), n3 + m6, n1) + subarray(buf3, n1, n5), n0 + m = 0, EB_PAGE_SIZE = 1, m = 1, n3 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 205:
# 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), subarray(buf2, 0, n2 + n3) = subarray(buf, 0, n2 + n3), 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, 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 ⊦ # buf = 1, subarray(buf2, n3, min(n1, n2)) + subarray(subarray(buf + mkempbuf(n0), n3, n1) + subarray(buf3, n1, n5), min(n1, n2), n4) = subarray(buf + mkempbuf(n0), n3, n1) + subarray(buf3, n1, n5), EB_PAGE_SIZE = 1, n3 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)% ⊦ m + n < m0 → m + n < m0 + n0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1; (ws)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 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% ⊦ m + n - m = n; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%m ≤ # buf ⊦ subarray(buf0 + buf, # buf0, m) = subarray(buf, 0, m); (s)% ⊦ m < n → m ≤ n; (s)%c: ⊦ m + n = n + m; from specification nat-basic