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Proof step 4 from proof put-same-content (previous step)

⊦ # ar[n, ar[n]] = # ar ∧ (∀ n0. n0 < # ar[n, ar[n]] → ar[n, ar[n]][n0] = ar[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n0 < # ar ⊦ ar[n, ar[n]][n0] = ar[n0], # ar = 0

Rule argument

Additional information

Used simplifier rules: Size-put: ⊦ # ar[n, a] = # ar;%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1