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Proof step 20 from proof cyclic-alt-def (conclusion)

⊦ cyclic(r, H) ↔ (∃ m, r0. reachable-n(H, m, r, r0) ∧ (∃ n. n ≠ 0 ∧ (∀ n0. reachable-n(H, m + n0 * n, r, r0))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ cyclic(r, H) ↔ (∃ m, n, r0. m < n ∧ reachable-n(H, m, r, r0) ∧ reachable-n(H, n, r, r0))
Proof step 19:
⊦ (∃ m, n, r0. m < n ∧ reachable-n(H, m, r, r0) ∧ reachable-n(H, n, r, r0)) ↔ (∃ m, r0. reachable-n(H, m, r, r0) ∧ (∃ n. n ≠ 0 ∧ (∀ n0. reachable-n(H, m + n0 * n, r, r0))))

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: cyclic-def antecedent: succedent: cyclic(r, H) ↔ (∃ m, n, r0. m < n ∧ reachable-n(H, m, r, r0) ∧ reachable-n(H, n, r, r0)) substlist: [H, r] → [H, r] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (H, r)]]