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Proof step 49 from proof cyclic-floyd-def (previous step)

reachable-n(H, n, r2, r2), reachable-n(H, n + m, r, r2), reachable-n(H, m * n, r, r1), reachable-n(H, m, r, r2), ∀ n0. reachable-n(H, m + n0 * n, r, r2) ⊦ n = 0, m = 0, reachable-n(H, 2 * m * n, r, r1)

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
⊦ reachable-n(H, n, r, r) ∧ reachable-n(H, m, r, r0) → (¬ reachable-n(H, n0 * n, r0, r0) ↔ false)
Proof step 48:
reachable-n(H, n, r2, r2) ∧ reachable-n(H, m * n - m, r2, r1) → (¬ reachable-n(H, (m + m - 1) * n, r1, r1) ↔ false), reachable-n(H, n, r2, r2), reachable-n(H, n + m, r, r2), reachable-n(H, m * n, r, r1), reachable-n(H, m, r, r2), ∀ n0. reachable-n(H, m + n0 * n, r, r2) ⊦ n = 0, m = 0, reachable-n(H, 2 * m * n, r, 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, n, r2, m * n - m, r1, m + m - 1] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (H, n, r2, m * n - m, r1, m + m - 1)]]