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Proof step 16 from proof cut (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])
Proof step 18:
# ar = 0 ⊦ 0 = # copy(subarray(ar, 1, 0 - 1), 0, mkarray(# subarray(ar, 1, 0 - 1) + 1), 1, # subarray(ar, 1, 0 - 1)) ∧ (n < 0 → ar[n] = copy(subarray(ar, 1, 0 - 1), 0, mkarray(# subarray(ar, 1, 0 - 1) + 1), 1, # subarray(ar, 1, 0 - 1))[0, ar[0]][n]), # ar = # [] ∧ (∀ n. n < # ar → ar[n] = ([])[n])

Rule argument

spec: array name: Extension seq: ⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]) subst: [ar2, ar1] → [[], ar] flags: <all paths>

Additional information

Used terms: [], ar