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Proof step 38 from proof valid-peb0-write-append (previous step)

# buf = LEB_SIZE, m + n + # buf0 = LEB_SIZE, subarray(buf, m, n + # buf0) = mkempbuf(n + # buf0), aehdr.valid?, (datasize(buf0) = 0 ⊃ datasize(buf, m);(m + n) + datasize(buf0)) < m4, (datasize(buf0) = 0 ⊃ datasize(buf, m);(m + n) + datasize(buf0)) < LEB_SIZE, (datasize(buf0) = 0 ⊃ datasize(buf, m);(m + n) + datasize(buf0)) < datasize(buf, m), is-aligned(m, EB_PAGE_SIZE), m4 ≤ LEB_SIZE, m4 ≤ datasize(buf, m), m + n ≤ LEB_SIZE ⊦ aehdr = empty

User applied rule case distinction

And closed the goal!

Rule argument

pos: left 6

Additional information

Used simplifier rules: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ m + m0 < n → ¬ n + n0 < m; (s)%n ≠ 0, m ≤ # buf ⊦ ¬ m + n < datasize(buf, m); (s)% ⊦ m ≤ n → (n < m ↔ false); (s)