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Proof step 17 from proof cyclic-floyd-def (previous step)

m = m2 +1, 2 * m = m0 + 1, reachable-n(H, (m1 + 1) + m, r, r2), reachable-n(H, m1 + 1, r2, r2), m * m1 ≤ m1 + 1, reachable-n(H, m, r, r2), reachable-n(H, m * m1 + m, r, r1), ∀ n. reachable-n(H, (n * m1 + n) + m, r, r2) ⊦ m = 0, reachable-n(H, 2 * (m * m1 + m), r, r1), reachable-n(H, m * m1, r2, r1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
reachable-n(H, (m2 + 1) + m1 * m2 + m1, r, r1), reachable-n(H, m2 + 1, r, r2), m1 * m2 ≤ 1, reachable-n(H, m1 + 1, r2, r2), reachable-n(H, 2 + m2 + m1, r, r2), ∀ n. reachable-n(H, (m2 + 1) + n * m1 + n, r, r2) ⊦ reachable-n(H, m1 * m2 + m1, r2, r1), reachable-n(H, 2 * (m1 * m2 + m2 + m1) + 2, r, r1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n ≤ m + n0 ↔ n ≤ n0], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : n < n0 ⊦ m + ((* n)) = m0 + ((* n0)) ↔ m = m0 + (n0 - n)], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m * (n + 1) = m * n + m], [CSIMPSEQ : ⊦ m +1 = m + 1])]]