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Proof step 9 from proof cyclic-weak-def (previous step)

reachable-n(H, m + n * n0, r, r0), reachable-n(H, m, r, r0), reachable-n(H, m + n * n0 - n, r1, r0), reachable-n(H, n, r, r1) ⊦ n0 = 0, ∃ r0. reachable-n(H, n, r, r0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
m + n * n0 = n1 + n ∧ n ≤ m + n * n0, reachable-n(H, m + n * n0, r, r0), reachable-n(H, m, r, r0), reachable-n(H, n1, r1, r0), reachable-n(H, n, r, r1) ⊦ n0 = 0, ∃ r0. reachable-n(H, n, r, r0)

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