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Proof step 13 from proof finz-bigger (previous step)

2 * (m0 + 1) = 2 * 2^ m2 * (1 + 2 * m), 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) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ m * n = m * n0 ↔ m = 0 ∨ n = n0
Proof step 12:
2 = 0 ∨ m0 + 1 = 2^ m2 * (1 + 2 * m), 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) ⊦

Rule argument

[x0lemmaarg: spec-name: nat-mult instance-name: lemma-name: zero-02 antecedent: succedent: m * n = m * n0 ↔ m = 0 ∨ n = n0 substlist: [n0, n, m] → [2^ m2 * (1 + 2 * m), m0 + 1, 2] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (2^ m2 * (1 + 2 * m), m0 + 1, 2)]]