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Proof step 24 from proof datasize-add-empty-h (previous step)

n0 + n < # buf, ¬ n < n → subarray(buf, n0, n + 1)[n] = mkempbuf(n + 1)[n], ∀ buf, n0. subarray(buf, n0, n) = mkempbuf(n) ∧ n0 + n ≤ # buf → datasize(buf, n0 + n) = datasize(buf, n0) ⊦ (n0 + n) + 1 = datasize(buf, n0), buf[n0 + n] = empty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
subarray(buf, n0, n + 1)[n] = mkempbuf(n + 1)[n], n0 + n < # buf, ∀ buf, n0. subarray(buf, n0, n) = mkempbuf(n) ∧ n0 + n ≤ # buf → datasize(buf, n0 + n) = datasize(buf, n0) ⊦ (n0 + n) + 1 = datasize(buf, n0), buf[n0 + n] = empty

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)