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Proof step 31 from proof cyclic-brent-def (previous step)

∃ m0. 2^ m0 ≤ m ∧ m < 2^ (m0 + 1), 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) ⊦ 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 30:
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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ 2 ^ n ≠ 0], [CSIMPSEQ : ⊦ 2 * m = 0 ↔ m = 0], [CSIMPFORWARD : ⊦ m ≤ n ∧ n < n0 → m < n0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m ^ (n + n0) = m ^ n * m ^ n0], [CSIMPSEQ : ⊦ 2^ m = 2 ^ m])]]