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Proof step 10 from proof cyclic-brent-def (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
2 ^ n = m0 + 1, cyclic(r, H), reachable-n(H, m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, n0 + m, r, r0), reachable-n(H, m0, r, r1), m ≤ m0, n0 ≤ m0, n0 ≤ m0 + 1 ⊦ n0 = 0, reachable-n(H, n0, r1, r1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m + n < m], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n ∧ m = n0 → n0 < n], [CSIMPFORWARD : ⊦ m < n ∧ n ≤ n0 → m < n0], [CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ 0 + m = m], [CSIMPSEQ : ⊦ n ≤ m → m + n0 - n = (m - n) + n0])]]