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Proof step 10 from proof cut (previous step)

⊦ ar = [], # ar = #(ar[0] + subarray(ar, 1, # ar - 1)) ∧ (n < # ar → ar[n] = (ar[0] + subarray(ar, 1, # ar - 1))[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ a + ar = copy(ar, 0, mkarray(# ar + 1), 1, # ar)[0, a]
Proof step 12:
⊦ ar = [], # ar = # copy(subarray(ar, 1, # ar - 1), 0, mkarray(# subarray(ar, 1, # ar - 1) + 1), 1, # subarray(ar, 1, # ar - 1))[0, ar[0]] ∧ (n < # ar → ar[n] = copy(subarray(ar, 1, # ar - 1), 0, mkarray(# subarray(ar, 1, # ar - 1) + 1), 1, # subarray(ar, 1, # ar - 1))[0, ar[0]][n])

Rule argument

spec: inst: name: cons seq: ⊦ a + ar = copy(ar, 0, mkarray(# ar + 1), 1, # ar)[0, a] subst: [ar, a] → [subarray(ar, 1, # ar - 1), ar[0]] flags: rewrite, current

Additional information

Used terms: subarray(ar, 1, # ar - 1), ar[0]