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Proof step 1 from proof sum-split (conclusion)

⊦ Σ(n, λ k. nf0(k) + nf1(k)) = Σ(n, nf0) + Σ(n, nf1)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ nf0, nf1. Σ(n0, λ k. nf0(k) + nf1(k)) = Σ(n0, nf0) + Σ(n0, nf1) ⊦ Σ(n0 +1, λ k. nf0(k) + nf1(k)) = Σ(n0 +1, nf0) + Σ(n0 +1, nf1)

Rule argument

term: n

Additional information

Used simplifier rules: sum-base: ⊦ Σ(0, nf) = 0;%nat freely generated by 0, +1;;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2