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Proof step 12 from proof subarray-split-size (previous step)

n2 < n0 + n1 ⊦ copy(ar, n, mkarray(n0 + n1), 0, n0 + n1)[n2] = (copy(ar, n, mkarray(n0), 0, n0) + copy(ar, n + n0, mkarray(n1), 0, n1))[n2]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])
Proof step 14:
n2 < n0 + n1, n2 < # mkarray(n0 + n1) ⊦ (n2 < 0 ∨ 0 + n0 + n1 ≤ n2 ⊃ mkarray(n0 + n1)[n2];ar[n2 + n - 0]) = (copy(ar, n, mkarray(n0), 0, n0) + copy(ar, n + n0, mkarray(n1), 0, n1))[n2]

Rule argument

spec: array-copy name: at-copy seq: ⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0]) subst: [m0, m, n0, ar1, n, ar0] → [n2, n0 + n1, 0, mkarray(n0 + n1), n, ar] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # mkarray(n) = n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n2, n0 + n1, 0, mkarray(n0 + n1), n, ar