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Proof step 10 from proof legal-noncylic-equiv-reaches-null (previous step)

H[r0] .nxt = null, legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, r ≠ null ∧ r ∈ H ∧ reachable*(H, r, r0), ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ reachable*(H, r, r0) ↔ (∃ n. reachable-n(H, n, r, r0))
Proof step 9:
H[r0] .nxt = null, legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, r ≠ null ∧ r ∈ H ∧ (∃ n. reachable-n(H, n, r, r0)), ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: reachable-star-def antecedent: succedent: reachable*(H, r, r0) ↔ (∃ n. reachable-n(H, n, r, r0)) substlist: [r0, r, H] → [r0, r, H] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1, 1, 1, 1, 1)) dummy: () ]

Additional information

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