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Proof step 45 from proof legal-noncylic-equiv-reaches-null (previous step)

H[r0] .nxt = null, ∀ n. ∃ r0. reachable-n(H, n, r, r0), reachable(r, r0, H), legal(H), r ∈ H, r0 ∈ H ⊦ r = null

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ reachable(r, r0, H) ↔ r ≠ null ∧ r ∈ H ∧ reachable*(H, r, r0)
Proof step 44:
H[r0] .nxt = null, ∀ n. ∃ r0. reachable-n(H, n, r, r0), r ≠ null ∧ r ∈ H ∧ reachable*(H, r, r0), legal(H), r ∈ H, r0 ∈ H ⊦ r = null

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: k-reachable-def antecedent: succedent: reachable(r, r0, H) ↔ r ≠ null ∧ r ∈ H ∧ reachable*(H, r, r0) substlist: [H, r0, r] → [H, r0, r] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

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