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Proof step 23 from proof cyclic-floyd-def (previous step)

∃ r2. reachable-n(H, n + m, r, r2) ∧ reachable-n(H, n1 + m - n + m, r2, r1), m * n = n1 + m, 2 * m = m0 + 1, reachable-n(H, n, r2, r2), reachable-n(H, n + m, r, r2), reachable-n(H, n1 + m, r, r1), reachable-n(H, m, r, r2), ∀ n0. reachable-n(H, m + n0 * n, r, r2) ⊦ n1 ≤ n, reachable-n(H, n1, r2, r1), n = 0, m = 0, reachable-n(H, 2 * (n1 + m), r, r1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
2 * m = m0 + 1, m * n = n1 + m, n < n1, reachable-n(H, n1 - n, r0, r1), reachable-n(H, m, r, r0), reachable-n(H, n1 + m, r, r1), reachable-n(H, n + m, r, r0), reachable-n(H, n, r0, r0), ∀ n0. reachable-n(H, m + n0 * n, r, r0) ⊦ m = 0, n = 0, reachable-n(H, 2 * (n1 + m), r, r1), reachable-n(H, n1, r0, r1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ reachable-n(H, n, r, r0) ∧ reachable-n(H, n, r, r1) → r0 = r1], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n - n + n1 = m - n1])]]