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Proof step 4 from proof put-rec (previous step)

n = m + 1 ⊦ x[n, a] = x.head ' + x.tail[m, a], n = 0, x = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ x[m + 1, a] = x.head ' + x.tail[m, a], x = []

Rule argument

Additional information

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