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Proof step 3 from proof put-rec (previous step)

n = m + 1 ⊦ x = [], n = 0, x[n, a] = x.first ' + x.rest[m, a]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ x = [], x[m + 1, a] = x.first ' + x.rest[m, a]

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2