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Proof step 19 from proof cyclic-floyd-def (previous step)

n = m1 +1, n1 ≤ n, 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) ⊦ reachable-n(H, n1, r2, r1), n = 0, m = 0, reachable-n(H, 2 * (n1 + m), r, r1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [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])]]