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Proof step 47 from proof cyclic-floyd-def (previous step)

reachable-n(H, n, r2, r2), reachable-n(H, n + m, r, r2), reachable-n(H, m * n, r, r1), reachable-n(H, m, r, r2), ∀ n0. reachable-n(H, m + n0 * n, r, r2), reachable-n(H, m * n - m, r2, r1) → reachable-n(H, (2 * m - 1) * n, r1, r1) ⊦ n = 0, m = 0, reachable-n(H, 2 * m * n, r, r1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 46:
2 * m = m0 + 1 ∧ 2 * m ≠ 0, reachable-n(H, n, r2, r2), reachable-n(H, n + m, r, r2), reachable-n(H, m * n, r, r1), reachable-n(H, m, r, r2), ∀ n0. reachable-n(H, m + n0 * n, r, r2), reachable-n(H, m * n - m, r2, r1) → reachable-n(H, m0 * n, r1, r1) ⊦ n = 0, m = 0, reachable-n(H, 2 * m * n, r, r1)

Rule argument

[x0lemmaarg: spec-name: nat instance-name: lemma-name: elim-pred-c antecedent: n ≠ 0 succedent: m = n - 1 ↔ n = m + 1 substlist: [n, m] → [2 * m, m0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 2 * m = 0 ↔ m = 0], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPELIM : n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1])], [EXTRATERMS : (2 * m, m0)]]