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Proof step 14 from proof datasize-add-empty-h (previous step)

buf[n0 + n] = empty, n0 + n < # buf, ∀ n1. ¬ n < n1 → subarray(buf, n0, n + 1)[n1] = mkempbuf(n + 1)[n1] ⊦ datasize(buf, n0 + n) = datasize(buf, n0), # subarray(buf, n0, n) = # mkempbuf(n) ∧ (∀ n1. n1 < # subarray(buf, n0, n) → subarray(buf, n0, n)[n1] = mkempbuf(n)[n1])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
buf[n0 + n] = empty, n1 < n, n0 + n < # buf, ∀ n1. ¬ n < n1 → subarray(buf, n0, n + 1)[n1] = mkempbuf(n + 1)[n1] ⊦ buf[n0 + n1] = empty, datasize(buf, n0 + n) = datasize(buf, n0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → mkempbuf(n)[m] = empty; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)