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Proof step 2 from proof dist (previous step)

∀ i, nf. i * Σ(n0, nf) = Σ(n0, λ k. i * nf(k)) ⊦ i * Σ(n0 +1, nf) = Σ(n0 +1, λ k. i * nf(k))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ i, nf. i * Σ(n0, nf) = Σ(n0, λ k. i * nf(k)) ⊦ Σ(n0, nf) * i = Σ(n0, λ k. i * nf(k))

Rule argument

Additional information

Used simplifier rules: sum-rec: ⊦ Σ(n + 1, nf) = nf(n) + Σ(n, nf);%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%eq-dist: ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0; from specification int-mult%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%succ: ⊦ m +1 = m + 1; from specification nat-basic2