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Proof step 5 from proof copy-rec (previous step)

n0 < # ar0 ⊦ copy(ar, m, ar0, m0, n)[m0 + n, ar[m + n]][n0] = copy(ar, m + 1, ar0, m0 + 1, n)[m0, ar[m]][n0], # ar0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ m ≠ n → ar[n, a][m] = ar[m]
Proof step 7:
¬ n0 ≠ m0 + n, n0 < # ar0 ⊦ copy(ar, m, ar0, m0, n)[m0 + n, ar[m + n]][n0] = copy(ar, m + 1, ar0, m0 + 1, n)[m0, ar[m]][n0], # ar0 = 0
Proof step 10:
n0 ≠ m0 + n, n0 < # ar0 ⊦ copy(ar, m, ar0, m0, n)[n0] = copy(ar, m + 1, ar0, m0 + 1, n)[m0, ar[m]][n0], # ar0 = 0

Rule argument

spec: array inst: name: Put-other seq: ⊦ m ≠ n → ar[n, a][m] = ar[m] subst: [m, a, n, ar] → [n0, ar[m + n], m0 + n, copy(ar, m, ar0, m0, n)] flags: rewrite

Additional information

Used terms: n0, ar[m + n], m0 + n, copy(ar, m, ar0, m0, n)