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Proof step 17 from proof cyclic-brent-def (previous step)

2 ^ n = m0 + 1, m ≤ m0, n0 ≤ m0, ∃ r0. reachable-n(H, m0, r, r0), ∀ n. ∃ r0. reachable-n(H, n, r, r0), reachable-n(H, m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, n0 + m, r, r0) ⊦ n0 = 0, ∃ r1. reachable-n(H, m0, r, r1), ∃ n, m, r0. m ≠ 0 ∧ m ≤ 2 ^ n ∧ reachable-n(H, 2 ^ n - 1, r, r0) ∧ reachable-n(H, m, r0, r0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
2 ^ n = m0 + 1, reachable-n(H, n0 + m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, m, r, r0), reachable-n(H, m0, r, r1), n0 ≤ m0, m ≤ m0, ∀ n. ∃ r0. reachable-n(H, n, r, r0) ⊦ n0 = 0, ∃ n, m, r0. m ≠ 0 ∧ m ≤ 2 ^ n ∧ reachable-n(H, 2 ^ n - 1, r, r0) ∧ reachable-n(H, m, r0, r0), ∃ r1. reachable-n(H, m0, r, r1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]