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Proof step 5 from proof finz-bounded-03 (previous step)

even(m), m < 2 * 2^ n, ∀ m1, n. m1 < m → (m1 < 2 * 2^ n → (n = #fz(m1) ↔ m1 + 1 = 2^ n)) ⊦ n = #fz(m) ↔ m + 1 = 2^ n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ even(n) ↔ (∃ m. m + m = n)
Proof step 4:
∃ m0. m0 + m0 = m, m < 2 * 2^ n, ∀ m1, n. m1 < m → (m1 < 2 * 2^ n → (n = #fz(m1) ↔ m1 + 1 = 2^ n)) ⊦ n = #fz(m) ↔ m + 1 = 2^ n

Rule argument

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