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Proof step 2 from proof sum-rec-01 (previous step)

⊦ ints = [], Σ ints = ints.first + Σ ints.rest

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: list-data inst: intlista name: elim-list-c seq: ints ≠ [] ⊦ i = ints.first ∧ ints0 = ints.rest ↔ ints = i + ints0 subst: [ints, i, ints0] → [ints, i, ints0] flags:

Additional information

Used simplifier rules: sum-app: ⊦ Σ(ints + ints0) = Σ ints + Σ ints0;%sum-one: ⊦ Σ i ' = i;%c: ⊦ i + ints = i ' + ints; from specification list[intlista]%e-01: ⊦ i ' + ints ≠ []; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%add-in: ⊦ i + j = i + i0 ↔ j = i0; 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%ints ≠ [] ⊦ i = ints.first ∧ ints0 = ints.rest ↔ ints = i + ints0; (elim) Used terms: ints, i, ints0