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Proof step 13 from proof datasize-samebuf-h (previous step)

m < # buf, n0 < # buf, (buf[n0] = empty ⊃ datasize(buf, n0);n0 + 1) < datasize(buf, m), (buf[n0] = empty ⊃ datasize(buf, n0);n0 + 1) < datasize(buf, n0), m ≤ n0, datasize(buf, m) ≤ datasize(buf, n0) ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 14:
n ≠ 0, m ≤ # buf ⊦ ¬ m + n < datasize(buf, m)

Rule argument

pos: left 3

Additional information

Used simplifier rules: datasize-ls-add: n ≠ 0, m ≤ # buf ⊦ ¬ m + n < datasize(buf, m);% ⊦ m < n → m ≤ n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → (n ≤ m ↔ false); (s)