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Proof step 22 from proof cyclic-floyd-def (previous step)

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)

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

[x0lemmaarg: spec-name: nat instance-name: lemma-name: elim-sub antecedent: n ≤ m succedent: n0 = m - n ↔ m = n0 + n substlist: [m, n, n0] → [n1, n, n2] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < n → ¬ n < m], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m < n → m ≤ n], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m < m + n ↔ n ≠ 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ reachable-n(H, n, r, r0) ∧ reachable-n(H, n0, r0, r1) → ( ¬ reachable-n (H, n + n0, r, r1) ↔ false)], [CSIMPELIM : n ≤ m ⊦ n0 = m - n ↔ m = n0 + n])], [EXTRATERMS : (n1, n, n2)]]