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Proof step 63 from proof cyclic-floyd-def (previous step)

reachable-n(H, m, r, r0), ∀ n0. reachable-n(H, m + n0 * n, r, r0) ⊦ n = 0, ∃ n, r0. n ≠ 0 ∧ reachable-n(H, n, r, r0) ∧ reachable-n(H, 2 * n, r, r0)

User applied rule cut formula

And obtained the following new goals

Proof step 57:
∃ r1. reachable-n(H, m * n, r, r1), reachable-n(H, m, r, r0), ∀ n0. reachable-n(H, m + n0 * n, r, r0) ⊦ n = 0, ∃ n, r0. n ≠ 0 ∧ reachable-n(H, n, r, r0) ∧ reachable-n(H, 2 * n, r, r0)
Proof step 62:
reachable-n(H, m, r, r0), ∀ n0. reachable-n(H, m + n0 * n, r, r0) ⊦ ∃ r1. reachable-n(H, m * n, r, r1), n = 0, ∃ n, r0. n ≠ 0 ∧ reachable-n(H, n, r, r0) ∧ reachable-n(H, 2 * n, r, r0)

Rule argument

[fma-arg: ∃ r1. reachable-n(H, m * n, r, r1)]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (∃ r1. reachable-n(H, m * n, r, r1))]]