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Proof step 14 from proof cyclic-weak-def (previous step)

cyclic(r, H) ⊦ ∃ r0. reachable-n(H, n, r, r0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ cyclic(r, H) ↔ (∃ m, r0. reachable-n(H, m, r, r0) ∧ (∃ n. n ≠ 0 ∧ (∀ n0. reachable-n(H, m + n0 * n, r, r0))))
Proof step 13:
∃ m, r0. reachable-n(H, m, r, r0) ∧ (∃ n. n ≠ 0 ∧ (∀ n0. reachable-n(H, m + n0 * n, r, r0))) ⊦ ∃ r0. reachable-n(H, n, r, r0)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: cyclic-alt-def antecedent: succedent: cyclic(r, H) ↔ (∃ m, r0. reachable-n(H, m, r, r0) ∧ (∃ n. n ≠ 0 ∧ (∀ n0. reachable-n(H, m + n0 * 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: ((0, 0, 0)) dummy: () ]

Additional information

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