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Proof step 6 from proof sum-swap (previous step)

∀ n, nnf. Σ(n, λ k0. Σ(m0, λ k1. nnf(k0, k1))) = Σ(m0, λ k1. Σ(n, λ k0. nnf(k0, k1))) ⊦ Σ(n, λ k. nnf(k, m0) + Σ(m0, λ k1. nnf(k, k1))) = Σ(n, λ k0. nnf(k0, m0)) + Σ(m0, λ k1. Σ(n, λ k0. nnf(k0, k1)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ Σ(n, λ k. nf0(k) + nf1(k)) = Σ(n, nf0) + Σ(n, nf1)
Proof step 8:
∀ n, nnf. Σ(n, λ k0. Σ(m0, λ k1. nnf(k0, k1))) = Σ(m0, λ k1. Σ(n, λ k0. nnf(k0, k1))) ⊦ Σ(n, λ n. nnf(n, m0)) + Σ(n, λ n. Σ(m0, λ k1. nnf(n, k1))) = Σ(n, λ k0. nnf(k0, m0)) + Σ(m0, λ k1. Σ(n, λ k0. nnf(k0, k1)))

Rule argument

spec: inst: name: sum-split seq: ⊦ Σ(n, λ k. nf0(k) + nf1(k)) = Σ(n, nf0) + Σ(n, nf1) subst: [nf1, nf0, n] → [λ n. Σ(m0, λ k1. nnf(n, k1)), λ n. nnf(n, m0), n] flags: rewrite, current

Additional information

Used terms: λ n. Σ(m0, λ k1. nnf(n, k1)), λ n. nnf(n, m0), n