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Proof step 15 from proof cyclic-all-cyclic (previous step)

reachable-n(H, n, r, r), reachable-n(H, m0 + 1, r, r0), ∀ H, n, r, r0. reachable-n(H, n, r, r) ∧ reachable-n(H, m0, r, r0) → reachable-n(H, n, r0, r0) ⊦ reachable-n(H, n, r0, r0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-1(H, r, r1) ∧ reachable-n(H, n, r1, r0))
Proof step 14:
reachable-n(H, n, r, r), ∃ r1. reachable-1(H, r, r1) ∧ reachable-n(H, m0, r1, r0), ∀ H, n, r, r0. reachable-n(H, n, r, r) ∧ reachable-n(H, m0, r, r0) → reachable-n(H, n, r0, r0) ⊦ reachable-n(H, n, r0, r0)

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: reachable-n-rec antecedent: succedent: reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-1(H, r, r1) ∧ reachable-n(H, n, r1, r0)) substlist: [r0, r, n, H] → [r0, r, m0, H] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r0, r, m0, H)]]