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Proof step 9 from proof cyclic-brent-def (previous step)

2 ^ n = m0 + 1, cyclic(r, H), reachable-n(H, m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, n0 + m, r, r0), reachable-n(H, m0, r, r1), m ≤ m0, n0 ≤ m0, n0 ≤ m0 + 1 ⊦ n0 = 0, reachable-n(H, n0, r1, r1)

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ reachable-n(H, n, r, r) ∧ reachable-n(H, m, r, r0) → (¬ reachable-n(H, n0 * n, r0, r0) ↔ false)
Proof step 8:
reachable-n(H, n0, r0, r0) ∧ reachable-n(H, m0 - m, r0, r1) → (¬ reachable-n(H, 1 * n0, r1, r1) ↔ false), 2 ^ n = m0 + 1, cyclic(r, H), reachable-n(H, m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, n0 + m, r, r0), reachable-n(H, m0, r, r1), m ≤ m0, n0 ≤ m0, n0 ≤ m0 + 1 ⊦ n0 = 0, reachable-n(H, n0, r1, r1)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: cyclic-all-ncyclic antecedent: succedent: reachable-n(H, n, r, r) ∧ reachable-n(H, m, r, r0) → (¬ reachable-n(H, n0 * n, r0, r0) ↔ false) substlist: [H, n, r, m, r0, n0] → [H, n0, r0, m0 - m, r1, 1] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (H, n0, r0, m0 - m, r1, 1)]]