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Proof step 12 from proof ls-datasize-zero (previous step)

# buf = n1 + n, n0 < n1 + n, ∀ n0. n0 < n → buf[n0] = empty ⊦ buf[n0] = (mkempbuf(n) + subarray(buf, n, n1))[n0], n0 < # mkempbuf(n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# buf = n1 + n, n0 < n1 + n, n ≤ n0, ∀ n0. n0 < n → buf[n0] = empty ⊦ buf[n0] = (mkempbuf(n) + subarray(buf, n, n1))[n0], n1 = 0

Rule argument

Additional information

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