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Proof step 10 from proof split-ok (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ odd(n) ↔ (∃ m. n = m + m + 1)
Proof step 9:
∃ m. n = m + m + 1, ∀ n0. n0 < n → (true → n0 + 1 = lead(n0) * 2 ^ #fz(n0)) ⊦ n + 1 = lead(n) * 2 ^ #fz(n)

Rule argument

[x0lemmaarg: spec-name: nat-even instance-name: lemma-name: oex antecedent: succedent: odd(n) ↔ (∃ m. n = m + m + 1) substlist: [n] → [n] 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 : (n)]]