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Proof step 24 from proof valid-peb0-write-append (previous step)

# buf = LEB_SIZE, LEB_SIZE = (n + # buf0) + m, aehdr.valid?, n0 < n, is-aligned(m, EB_PAGE_SIZE), m + n ≤ LEB_SIZE, m4 ≤ datasize(buf), m4 ≤ LEB_SIZE, m ≤ LEB_SIZE, ∀ n1. n1 < n + # buf0 → buf[m + n1] = empty ⊦ buf[m + n0] = empty, aehdr = empty, m4 = 0, m4 ≤ (datasize(buf0) = 0 ⊃ datasize(buf, m + n);(m + n) + datasize(buf0)) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m + n) + buf0, m4)

User applied rule all left

And closed the goal!

Rule argument

pos: left 10 terms: n0 abort: F discard: T computed: F

Additional information

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