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Proof step 6 from proof subarray-emparray (previous step)

n < n2, n < n1, n2 ≤ n1 ⊦ fill(mkarray(n0 + n1), empty)[n0 + n] = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ n < # ar → fill(ar, a)[n] = a

Rule argument

spec: array-copy name: at-fill seq: ⊦ n < # ar → fill(ar, a)[n] = a subst: [n, a, ar] → [n0 + n, empty, mkarray(n0 + n1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # mkarray(n) = n; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n0 + n, empty, mkarray(n0 + n1)