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Proof step 42 from proof cyclic-floyd-def (previous step)

reachable-n(H, m0 * n, r1, r1), m * n = n1 + m, 2 * m = m0 + 1, reachable-n(H, n, r2, r2), reachable-n(H, n + m, r, r2), reachable-n(H, n1 + m, 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 * (n1 + m), r, r1)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 26:
⊦ reachable-n(H, n, r, r0) ∧ reachable-n(H, n0, r0, r1) → (¬ reachable-n(H, n + n0, r, r1) ↔ false)
Proof step 41:
reachable-n(H, n1 + m, r, r1) ∧ reachable-n(H, n1 + m, r1, r1) → (¬ reachable-n(H, (n1 + m) + n1 + m, r, r1) ↔ false), reachable-n(H, m0 * n, r1, r1), m * n = n1 + m, 2 * m = m0 + 1, reachable-n(H, n, r2, r2), reachable-n(H, n + m, r, r2), reachable-n(H, n1 + m, 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 * (n1 + m), r, r1)

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: reachable-n-trans antecedent: succedent: reachable-n(H, n, r, r0) ∧ reachable-n(H, n0, r0, r1) → (¬ reachable-n(H, n + n0, r, r1) ↔ false) substlist: [H, n, r, r0, n0, r1] → [H, n1 + m, r, r1, n1 + m, r1] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (H, n1 + m, r, r1, n1 + m, r1)]]