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Proof step 30 from proof cyclic-brent-def (previous step)

2 ^ m1 < 2 ^ m1 * 2, m < 2 ^ m1 * 2, 2 ^ m1 ≤ m, reachable-n(H, n0 + m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, m, r, r0), cyclic(r, H), 2 ^ m0 ≤ n0, n0 < 2 ^ m0 * 2, 2 ^ m0 < 2 ^ m0 * 2 ⊦ n0 = 0, ∃ n, m, r0. m ≠ 0 ∧ m ≤ 2 ^ n ∧ reachable-n(H, 2 ^ n - 1, r, r0) ∧ reachable-n(H, m, r0, r0), ∃ n. ¬ 2 ^ n ≤ n0 ∧ ¬ 2 ^ n ≤ m

User applied rule exists right

And obtained the following new goals

Proof step 29:
2 ^ m1 < 2 ^ m1 * 2, m < 2 ^ m1 * 2, 2 ^ m1 ≤ m, reachable-n(H, n0 + m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, m, r, r0), cyclic(r, H), 2 ^ m0 ≤ n0, n0 < 2 ^ m0 * 2, 2 ^ m0 < 2 ^ m0 * 2 ⊦ n0 = 0, ∃ n, m, r0. m ≠ 0 ∧ m ≤ 2 ^ n ∧ reachable-n(H, 2 ^ n - 1, r, r0) ∧ reachable-n(H, m, r0, r0), ¬ 2 ^ (m1 + 1) ≤ n0 ∧ ¬ 2 ^ (m1 + 1) ≤ m, ∃ n. ¬ 2 ^ n ≤ n0 ∧ ¬ 2 ^ n ≤ m

Rule argument

[EXRARG : pos: right 3, [extquanttermlist: (m1 + 1)abort:F, discard:F, computed:F]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (m1 + 1)]]