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Proof step 40 from proof cyclic-brent-def (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 2:
reachable-n(H, n, r, r0), m < n ⊦ ∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n - m, r1, r0)
Proof step 39:
∃ r1. reachable-n(H, m, r, r1) ∧ reachable-n(H, n - m, r1, r0), reachable-n(H, n, r, r0), reachable-n(H, m, r, r0), m < n, cyclic(r, H) ⊦ ∃ 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: path-reachable instance-name: lemma-name: reach-n-split 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, n, r, r0, m] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (H, n, r, r0, m)]]