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Proof step 8 from proof cyclic-brent-def (previous step)

reachable-n(H, n0, r0, r0) ∧ reachable-n(H, m0 - m, r0, r1) → (¬ reachable-n(H, 1 * n0, r1, r1) ↔ false), 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
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), reachable-n(H, m0 - m, r0, r1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m0 * 1 = m0])]]