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Proof step 2 from proof sum-app (previous step)

∀ ints0. Σ(ints1 + ints0) = Σ ints1 + Σ ints0 ⊦ Σ((i + ints1) + ints0) = Σ(i + ints1) + Σ ints0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ ints0. Σ(ints1 + ints0) = Σ ints1 + Σ ints0 ⊦ Σ(ints1 + ints0) = Σ ints1 + Σ ints0

Rule argument

Additional information

Used simplifier rules: sum-rec: ⊦ Σ(i ' + ints) = i + Σ ints;%add-c: ⊦ i + j = j + i; from specification int-basic2%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%c: ⊦ i + ints = i ' + ints; from specification list[intlista]