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Proof step 4 from proof put-both-eq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n < # ar, ∀ n0. n0 < # ar → ar[n, a][n0] = ar[n, b][n0] ⊦ a = b, # ar = 0

Rule argument

Additional information

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