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Proof step 40 from proof cyclic-floyd-def (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 36:
m * n = n1 + m, 2 * m = m0 + 1, reachable-n(H, m0 * n, r1, r1), 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 + m, r1, r1), n = 0, m = 0, reachable-n(H, 2 * (n1 + m), r, r1)
Proof step 39:
reachable-n(H, (m0 + 1) + 2 * n1, r, r1), m * n = n1 + m, 2 * m = m0 + 1, reachable-n(H, m0 * n, r1, r1), 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

[CASEDARG : pos: left 9, ()]

Additional information

[[CONCRETESIMPRULES : ()]]