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Proof step 3 from proof Sep-distribute-true (previous step)

∀ nP, n. nP ⊗_(n, m0) * true = (λ n0. nP(n0) * true)⊗_(n, m0) * true ⊦ nP ⊗_(n, m0 + 1) * true = (λ n0. nP(n0) * true)⊗_(n, m0 + 1) * true

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ nP ⊗_(n, m + 1) = nP(n) * nP ⊗_(n + 1, m)
Proof step 5:
∀ nP, n. nP ⊗_(n, m0) * true = (λ n0. nP(n0) * true)⊗_(n, m0) * true ⊦ (nP(n) * nP ⊗_(n + 1, m0)) * true = (λ n0. nP(n0) * true)⊗_(n, m0 + 1) * true

Rule argument

spec: <toplevel> name: Sep-rec seq: ⊦ nP ⊗_(n, m + 1) = nP(n) * nP ⊗_(n + 1, m) subst: [m, n, nP] → [m0, n, nP] flags: <all paths>

Additional information

Used terms: m0, n, nP