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Proof step 28 from proof split-unique (previous step)

(2 ^ #fz(m0) * 2) * lead(m0) = lead(m) * 2 ^ #fz(m), odd(m), ∀ n0, m. n0 < m0 + m0 + 1 → (lead(n0) * 2 ^ #fz(n0) = lead(m) * 2 ^ #fz(m) → m = n0) ⊦ m = 2 * m0 + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ odd(n) ↔ (∃ m. n = m + m + 1)
Proof step 27:
(2 ^ #fz(m0) * 2) * lead(m0) = lead(m) * 2 ^ #fz(m), ∃ m0. m = m0 + m0 + 1, ∀ n0, m. n0 < m0 + m0 + 1 → (lead(n0) * 2 ^ #fz(n0) = lead(m) * 2 ^ #fz(m) → m = n0) ⊦ m = 2 * m0 + 1

Rule argument

[x0lemmaarg: spec-name: nat-even instance-name: lemma-name: oex antecedent: succedent: odd(n) ↔ (∃ m. n = m + m + 1) substlist: [n] → [m] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (m)]]