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Proof step 25 from proof cyclic-floyd-def (previous step)

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)

User applied rule cut formula

And obtained the following new goals

Proof step 20:
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)
Proof step 24:
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) ⊦ n1 ≤ n, reachable-n(H, n1, r2, r1), n = 0, m = 0, reachable-n(H, 2 * (n1 + m), r, r1)

Rule argument

[fma-arg: n1 ≤ n]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (n1 ≤ n)]]