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Proof step 33 from proof cyclic-floyd-def (previous step)

2 * m = m0 + 1, reachable-n(H, m0 * n, r1, r1), 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) ⊦ n = 0, m = 0, reachable-n(H, m * n, r1, r1), reachable-n(H, 2 * m * n, r, r1), reachable-n(H, m * n - m, r2, r1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
m * n = n1 + m ∧ m ≤ m * n, 2 * m = m0 + 1, reachable-n(H, m0 * n, r1, r1), 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) ⊦ n = 0, m = 0, reachable-n(H, m * n, r1, r1), reachable-n(H, 2 * m * n, r, r1), reachable-n(H, n1, r2, r1)

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] → [m * n, m, n1] 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 ≠ 0], [CSIMPSEQ : ⊦ m0 * m < m ↔ m0 = 0 ∧ m ≠ 0], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPELIM : n ≤ m ⊦ n0 = m - n ↔ m = n0 + n])], [EXTRATERMS : (m * n, m, n1)]]