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Proof step 1 from proof put-rec-02 (conclusion)

⊦ n ≠ 0 → (a ' + x)[n, b] = a ' + x[n -1, b]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ n = 0, (a ' + x)[n, b] = a ' + x[n - 1, b]

Rule argument

Additional information

Used simplifier rules: pred-03: ⊦ n -1 = n - 1; from specification nat