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Proof step 7 from proof Sep-distribute-true (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ nP, n. nP ⊗_(n, m0) * true = (λ n0. nP(n0) * true)⊗_(n, m0) * true ⊦ (nP(n) * nP ⊗_(n + 1, m0)) * true = true * nP(n) * (λ n0. nP(n0) * true)⊗_(n + 1, m0)

Rule argument

Additional information

Used simplifier rules: sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep% ⊦ true * true = true; (s)