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Proof step 7 from proof cyclic-brent-def (previous step)

2 ^ n = m0 + 1, cyclic(r, H), reachable-n(H, m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, n0 + m, r, r0), reachable-n(H, m0, r, r1), m ≤ m0, n0 ≤ m0, n0 ≤ m0 + 1 ⊦ n0 = 0, reachable-n(H, n0, r1, r1), reachable-n(H, m0 - m, r0, r1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
m0 = n1 + m, 2 ^ n = m0 + 1, cyclic(r, H), reachable-n(H, m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, n0 + m, r, r0), reachable-n(H, m0, r, r1), m ≤ m0, n0 ≤ m0, n0 ≤ m0 + 1 ⊦ n0 = 0, reachable-n(H, n0, r1, r1), reachable-n(H, n1, r0, 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] → [m0, m, n1] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : n ≤ m ⊦ n0 = m - n ↔ m = n0 + n])], [EXTRATERMS : (m0, m, n1)]]