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Proof step 36 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) ⊦ n0 = 0, ∃ n, m, r0. m ≠ 0 ∧ m ≤ 2 ^ n ∧ reachable-n(H, 2 ^ n - 1, r, r0) ∧ reachable-n(H, m, r0, r0)

User applied rule cut formula

And obtained the following new goals

Proof step 23:
∃ n. 2 ^ n > n0 ∧ 2 ^ n > m, 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)
Proof step 35:
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)

Rule argument

[fma-arg: ∃ n. 2 ^ n > n0 ∧ 2 ^ n > m]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (∃ n. 2 ^ n > n0 ∧ 2 ^ n > m)]]