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Proof step 2 from proof put-same-content (previous step)

⊦ ar[n, ar[n]] = ar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])
Proof step 4:
⊦ # ar[n, ar[n]] = # ar ∧ (∀ n0. n0 < # ar[n, ar[n]] → ar[n, ar[n]][n0] = ar[n0])

Rule argument

spec: inst: name: Extension seq: ⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]) subst: [ar2, ar1] → [ar, ar[n, ar[n]]] flags: rewrite, current

Additional information

Used terms: ar, ar[n, ar[n]]