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Proof step 14 from proof split-unique-2 (previous step)

2^ n * n0 = 2^ #fz(m) * lead(m), odd(n0), odd(m), ∀ m1, n, n0. m1 < m → (2^ n * n0 = 2^ #fz(m1) * lead(m1) ∧ odd(n0) → n = #fz(m1) ∧ n0 = lead(m1)) ⊦ n = #fz(m) ∧ n0 = lead(m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ odd(n) ↔ (∃ m. n = m + m + 1)
Proof step 13:
2^ n * n0 = 2^ #fz(m) * lead(m), odd(n0), ∃ m0. m = m0 + m0 + 1, ∀ m1, n, n0. m1 < m → (2^ n * n0 = 2^ #fz(m1) * lead(m1) ∧ odd(n0) → n = #fz(m1) ∧ n0 = lead(m1)) ⊦ n = #fz(m) ∧ n0 = lead(m)

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, 2)) dummy: () ]

Additional information

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