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Proof step 25 from proof cyclic-weak-def (previous step)

reachable-n(H, # H + 1, r, r0), ∀ n. ∃ r0. reachable-n(H, n, r, r0) ⊦ cyclic(r, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ n ≠ 0 → (reachable-n(H, n, r, r0) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x .last = r0 ∧ # x = n + 1))
Proof step 24:
# H + 1 ≠ 0, ∃ x. path(x, H) ∧ hd x = r ∧ x .last = r0 ∧ # x = (# H + 1) + 1, ∀ n. ∃ r0. reachable-n(H, n, r, r0) ⊦ cyclic(r, H)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (r0, r, # H + 1, H)]]