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Proof step 4 from proof cyclic-alt-def (previous step)

∀ H, n1, m, r, r0. reachable-n(H, n1 + m, r, r0) ∧ reachable-n(H, n1, r0, r0) ∧ reachable-n(H, m, r, r0) → n1 = 0 ∨ reachable-n(H, m + n0 * n1, r, r0), reachable-n(H, n1 + m, r, r0), reachable-n(H, n1, r0, r0), reachable-n(H, m, r, r0) ⊦ n1 = 0, reachable-n(H, m + n0 +1 * n1, r, r0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
reachable-n(H, n1 + m, r, r0), reachable-n(H, n1, r0, r0), reachable-n(H, m, r, r0), ∀ H0, n, m0, r1, r2. reachable-n(H0, n, r2, r2) ∧ reachable-n(H0, m0, r1, r2) → n = 0 ∨ reachable-n(H0, m0 + n0 * n, r1, r2) ⊦ n1 = 0, reachable-n(H, (n1 * n0 + n1) + m, r, r0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ reachable-n(H, n, r, r0) ∧ reachable-n(H, n0, r0, r1) → ( ¬ reachable-n (H, n + n0, r, r1) ↔ false)], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m * (n + 1) = m * n + m], [CSIMPSEQ : ⊦ m +1 = m + 1])]]