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Proof step 7 from proof Sep-unfold (previous step)

⊦ nP ⊗_(n, (m + 1) + m0) = nP ⊗_(n, m0) * nP(n + m0) * nP ⊗_(n + m0 + 1, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ m0 ≤ m → nP ⊗_(n, m) = nP ⊗_(n, m0) * nP ⊗_(n + m0, m - m0)
Proof step 9:
m0 ≤ (m + 1) + m0 ⊦ nP ⊗_(n, m0) * nP ⊗_(n + m0, (m + 1) + m0 - m0) = nP ⊗_(n, m0) * nP(n + m0) * nP ⊗_(n + m0 + 1, m)

Rule argument

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

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m0, (m + 1) + m0, n, nP