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Proof step 5 from proof cyclic-brent-def (previous step)

2 ^ n = (n1 + m) + 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, n1 + m, r, r1), n0 ≤ n1 + m, n0 ≤ 2 ^ n ⊦ n0 = 0, reachable-n(H, n0, r1, r1), reachable-n(H, n1, r0, r1)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 4:
reachable-n(H, n, r, r0), m ≤ n ⊦ ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n - m, r1, r0)

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: reach-n-split-le antecedent: reachable-n(H, n, r, r0), m ≤ n succedent: ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n - m, r1, r0) substlist: [H, n, r, r0, m] → [H, n1 + m, r, r1, m] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m + n < m], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m + n - m = n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPFORWARD : ⊦ reachable-n(H, n, r, r0) ∧ reachable-n(H, n, r, r1) → r0 = r1])], [EXTRATERMS : (H, n1 + m, r, r1, m)]]