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Proof step 73 from proof path-dups (previous step)

(r ' + x1)[m] = (r ' + x1)[n], path(r ' + x1, H), n ≤ # x1, m ≤ # x1 ⊦ m = n, cyclic(r, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ cyclic(r, H) ↔ (∃ m, n, r0. m < n ∧ reachable-n(H, m, r, r0) ∧ reachable-n(H, n, r, r0))
Proof step 72:
(r ' + x1)[m] = (r ' + x1)[n], path(r ' + x1, H), n ≤ # x1, m ≤ # x1 ⊦ m = n, ∃ m, n, r0. m < n ∧ reachable-n(H, m, r, r0) ∧ reachable-n(H, 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, 1)) dummy: () ]

Additional information

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