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Proof step 1 from proof put-rec-01 (conclusion)

⊦ n ≠ 0 ∧ x ≠ [] → x[n, a] = x.first ' + x.rest[n -1, a]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ x = [], n = 0, x[n, a] = x.first ' + x.rest[n - 1, a]

Rule argument

Additional information

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