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Proof step 18 from proof subarray-split-size (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])
Proof step 20:
n2 < n0 + n1 ⊦ ar[n2 + n] = (n2 < n0 ⊃ copy(ar, n, mkarray(n0), 0, n0)[n2];copy(ar, n + n0, mkarray(n1), 0, n1)[n2 - n0]), n2 < # mkarray(n0)

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, 0, mkarray(n0), n, ar] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ m < 0; (s)% ⊦ n + 0 = n; (s)%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)% ⊦ m - 0 = m; (s)% ⊦ # mkarray(n) = n; (s) Used terms: n2, n0, 0, mkarray(n0), n, ar