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Proof step 13 from proof cyclic-brent-def (previous step)

reachable-n(H, n0 + m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, m, r, r0), cyclic(r, H), n0 < 2 ^ n, m < 2 ^ n, reachable-n(H, 2 ^ n - 1, r, r1) ⊦ n0 = 0, ∃ n, m, r0. m ≠ 0 ∧ m ≤ 2 ^ n ∧ reachable-n(H, 2 ^ n - 1, r, r0) ∧ reachable-n(H, m, r0, r0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
2 ^ n = m0 + 1 ∧ 2 ^ n ≠ 0, reachable-n(H, n0 + m, r, r0), reachable-n(H, n0, r0, r0), reachable-n(H, m, r, r0), cyclic(r, H), n0 < 2 ^ n, m < 2 ^ n, reachable-n(H, m0, r, r1) ⊦ n0 = 0, ∃ n, m, r0. m ≠ 0 ∧ m ≤ 2 ^ n ∧ reachable-n(H, 2 ^ n - 1, r, r0) ∧ reachable-n(H, m, r0, r0)

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 ^ n, m0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

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