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Proof step 12 from proof finz-bounded (previous step)

(m + m0) + n0 = 2^ #fz(m), m + 1 = ((m + m0) + n0) * (2 * m1 + 1), m + m0 = 2^ n, lead(m) = 2 * m1 + 1, n < #fz(m) ⊦ m0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 11:
(m + m0) + n0 = 2^ #fz(m), m + 1 = ((m + m0) + n0) * 2 * m1 + ((m + m0) + n0) * 1, m + m0 = 2^ n, lead(m) = 2 * m1 + 1, n < #fz(m) ⊦ m0 = 0

Rule argument

[x0lemmaarg: spec-name: nat-mult instance-name: lemma-name: dist antecedent: succedent: m0 * (m + n) = m0 * m + m0 * n substlist: [n, m, m0] → [1, 2 * m1, (m + m0) + n0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1, 1, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (1, 2 * m1, (m + m0) + n0)]]