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Proof step 14 from proof cyclic-floyd-def (previous step)

m1 * m2 = 0, reachable-n(H, 2 + m2 + m1, r, r2), reachable-n(H, m1 + 1, r2, r2), reachable-n(H, m2 + 1, r, r2), reachable-n(H, 1 + m2 + m1, r, r1), ∀ n. reachable-n(H, (m2 + 1) + n * m1 + n, r, r2) ⊦ reachable-n(H, 2 + 2 * (m2 + m1), r, r1), reachable-n(H, m1, r2, r1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0
Proof step 13:
m1 = 0 ∨ m2 = 0, reachable-n(H, 2 + m2 + m1, r, r2), reachable-n(H, m1 + 1, r2, r2), reachable-n(H, m2 + 1, r, r2), reachable-n(H, 1 + m2 + m1, r, r1), ∀ n. reachable-n(H, (m2 + 1) + n * m1 + n, r, r2) ⊦ reachable-n(H, 2 + 2 * (m2 + m1), r, r1), reachable-n(H, m1, r2, r1)

Rule argument

[x0lemmaarg: spec-name: nat-mult instance-name: lemma-name: zero-01 antecedent: succedent: m0 * m = 0 ↔ m0 = 0 ∨ m = 0 substlist: [m, m0] → [m2, m1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (m2, m1)]]