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Proof step 70 from proof cyclic-floyd-def (previous step)

⊦ cyclic(r, H) ↔ (∃ n, r0. n ≠ 0 ∧ reachable-n(H, n, r, r0) ∧ reachable-n(H, 2 * n, r, r0))

User applied rule case distinction

And obtained the following new goals

Proof step 65:
cyclic(r, H) ⊦ ∃ n, r0. n ≠ 0 ∧ reachable-n(H, n, r, r0) ∧ reachable-n(H, 2 * n, r, r0)
Proof step 69:
∃ n, r0. n ≠ 0 ∧ reachable-n(H, n, r, r0) ∧ reachable-n(H, 2 * n, r, r0) ⊦ cyclic(r, H)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]