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Proof step 10 from proof finz-bounded-05 (previous step)

n * 2^ n0 ≤ m, m + 1 < 2^ n0 * n + 2^ n0, n0 ≤ #fz(m), odd(m), ∀ m1, n0, n. m1 < m → (n0 ≤ #fz(m1) ∧ m1 + 1 < 2^ n0 * n + 2^ n0 ∧ n * 2^ n0 ≤ m1 → false) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ odd(n) ↔ (∃ m. n = m + m + 1)
Proof step 9:
n * 2^ n0 ≤ m, m + 1 < 2^ n0 * n + 2^ n0, n0 ≤ #fz(m), ∃ m0. m = m0 + m0 + 1, ∀ m1, n0, n. m1 < m → (n0 ≤ #fz(m1) ∧ m1 + 1 < 2^ n0 * n + 2^ n0 ∧ n * 2^ n0 ≤ m1 → false) ⊦

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, 3)) dummy: () ]

Additional information

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