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Proof step 35 from proof cyclic-brent-def (previous step)

reachable-n(H, n0 + m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, m, r, r0), cyclic(r, H) ⊦ ∃ n. 2 ^ n > n0 ∧ 2 ^ n > m, n0 = 0, ∃ 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 34:
reachable-n(H, n0 + m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, m, r, r0), cyclic(r, H) ⊦ 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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ m > n ↔ n < m])]]