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Proof step 10 from proof subarray-append-mkempbuf-from (previous step)

n < n2, n < n1 + # buf, n2 ≤ n1 + # buf ⊦ (n < n1 ⊃ mkempbuf(n0 + n1)[n0 + n];buf[n - n1]) = (n < n1 ⊃ empty;buf[n - n1])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ m < n → mkempbuf(n)[m] = empty

Rule argument

spec: array-splice, inst: buffer name: emparray-at seq: ⊦ m < n → mkempbuf(n)[m] = empty subst: [m, n] → [n0 + n, n0 + n1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%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) Used terms: n0 + n, n0 + n1