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Proof step 33 from proof legal-noncylic-equiv-reaches-null (previous step)

r ∈ H, legal(H) ⊦ r = null, cyclic(r, H), ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ cyclic(r, H) ↔ (∀ n. ∃ r0. reachable-n(H, n, r, r0))
Proof step 32:
r ∈ H, legal(H) ⊦ r = null, ∀ n. ∃ r0. reachable-n(H, n, r, r0), ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: cyclic-weak-def antecedent: succedent: cyclic(r, H) ↔ (∀ n. ∃ 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, 1)) dummy: () ]

Additional information

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