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Proof step 4 from proof copy-append (previous step)

n0 < # ar1 ⊦ copy(ar0, n + m1, copy(ar0, n, ar1, n1, m1), n1 + m1, m0)[n0] = (n0 < n1 ∨ n1 + m0 + m1 ≤ n0 ⊃ ar1[n0];ar0[n0 + n - n1]), # ar1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])
Proof step 6:
n0 < # copy(ar0, n, ar1, n1, m1), n0 < # ar1 ⊦ (n0 < n1 + m1 ∨ (n1 + m1) + m0 ≤ n0 ⊃ copy(ar0, n, ar1, n1, m1)[n0];ar0[n0 + n + m1 - n1 + m1]) = (n0 < n1 ∨ n1 + m0 + m1 ≤ n0 ⊃ ar1[n0];ar0[n0 + n - n1]), # ar1 = 0

Rule argument

spec: inst: 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] → [n0, m0, n1 + m1, copy(ar0, n, ar1, n1, m1), n + m1, ar0] flags: rewrite, current

Additional information

Used simplifier rules: size-copy: ⊦ # copy(ar, m, ar0, m0, n) = # ar0;%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: n0, m0, n1 + m1, copy(ar0, n, ar1, n1, m1), n + m1, ar0