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Proof step 1 from proof sum-one (conclusion)

⊦ Σ i ' = i

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
⊦ Σ(i ' + ints) = i + Σ ints

Rule argument

spec: intlist inst: name: sum-rec seq: ⊦ Σ(i ' + ints) = i + Σ ints subst: [i, ints] → [i, []] flags: current, []

Additional information

Used simplifier rules: sum-empty: ⊦ Σ [] = 0;%app: ⊦ 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 Used terms: i, []