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Proof step 13 from proof ls-datasize-wear-level (previous step)

# buf = LEB_SIZE, LEB_SIZE = n1 + m, subarray(buf, m, n1) = mkempbuf(n1), m < datasize(buf, LEB_SIZE), is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE, m < LEB_SIZE → buf = subarray(buf, 0, m) + subarray(buf, m, n1) ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 14:
# buf = LEB_SIZE, LEB_SIZE = n1 + m, buf = subarray(buf, 0, m) + subarray(buf, m, n1), subarray(buf, m, n1) = mkempbuf(n1), m < datasize(buf, LEB_SIZE), is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE ⊦

Rule argument

pos: left 7

Additional information

Used simplifier rules: nat-sum-leq: ⊦ m = n0 + n1 → (m ≤ n1 ↔ n0 = 0);% ⊦ m < n ↔ ¬ n ≤ m; (ss)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ ¬ n < datasize(buf, n); (s)