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Proof step 44 from proof cyclic-floyd-def (previous step)

m * n = n1 + m ∧ m ≤ m * n, 2 * m = m0 + 1, 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), reachable-n(H, n1, r2, r1) → reachable-n(H, m0 * n, r1, r1) ⊦ n = 0, m = 0, reachable-n(H, 2 * m * n, r, r1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
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) → reachable-n(H, m0 * n, r1, r1) ⊦ n = 0, m = 0, reachable-n(H, 2 * (n1 + m), r, r1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m0 ≠ 0 → m ≤ m * m0])]]