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Proof step 27 from proof cyclic-brent-def (previous step)

2 ^ m0 < 2 ^ m0 * 2, n0 < 2 ^ m0 * 2, 2 ^ m0 ≤ n0, cyclic(r, H), reachable-n(H, m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, n0 + m, r, r0) ⊦ m ≠ 0, n0 = 0, ∃ n. ¬ 2 ^ n ≤ n0 ∧ ¬ 2 ^ n ≤ m, ∃ 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 26:
reachable-n(H, n0, r0, r0), cyclic(r0, H), 2 ^ m0 ≤ n0, n0 < 2 ^ m0 * 2, 2 ^ m0 < 2 ^ m0 * 2 ⊦ n0 = 0, ∃ n. ¬ 2 ^ n ≤ n0, ∃ n, m, r1. m ≠ 0 ∧ m ≤ 2 ^ n ∧ reachable-n(H, 2 ^ n - 1, r0, r1) ∧ reachable-n(H, m, r1, r1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 2 ^ n ≠ 0], [CSIMPSEQ : ⊦ m ≤ 0 ↔ m = 0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ 0 + m = m], [CSIMPSEQ : ⊦ reachable-n(H, 0, r, r0) ↔ r = r0])]]