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Proof step 25 from proof datasize-add-empty-h (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]

Rule argument

spec: array-copy, inst: buffer name: subarray-at seq: ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0] subst: [n0, n, m, buf] → [n, n + 1, n0, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n → mkempbuf(n)[m] = empty; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n, n + 1, n0, buf