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Proof step 1 from proof sum-app (conclusion)

⊦ Σ(ints + ints0) = Σ ints + Σ ints0

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ ints0. Σ(ints1 + ints0) = Σ ints1 + Σ ints0 ⊦ Σ((i + ints1) + ints0) = Σ(i + ints1) + Σ ints0

Rule argument

indvar: ints

Additional information

Used simplifier rules: sum-empty: ⊦ Σ [] = 0;%intlist freely generated by [], +;;%Nil: ⊦ [] + ints = ints; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%ax-04: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2