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Proof step 15 from proof finz-bigger (previous step)

2 * m0 + 2 = 2 * 2^ m2 + 4 * 2^ m2 * m, #fz(m0) < m2, ∀ m1, n, n0. m1 < m0 + m0 + 1 → (m1 + 1 = n * 2^ n0 ∧ #fz(m1) < n0 → false) ⊦ 2 * m0 + 2 = (4 * m + 2) * 2^ m2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ m0 * (m + n) = m0 * m + m0 * n

Rule argument

[x0lemmaarg: spec-name: nat-mult instance-name: lemma-name: dist antecedent: succedent: m0 * (m + n) = m0 * m + m0 * n substlist: [m0, n, m] → [2^ m2, 2, 4 * m] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ m * n = n * m])], [EXTRATERMS : (2^ m2, 2, 4 * m)]]