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Proof step 48 from proof legal-noncylic-equiv-reaches-null (conclusion)

legal(H), r ∈ H, r ≠ null ⊦ ¬ cyclic(r, H) ↔ (∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null)

User applied rule case distinction

And obtained the following new goals

Proof step 34:
¬ cyclic(r, H), legal(H), r ∈ H, r ≠ null ⊦ ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null
Proof step 47:
∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, legal(H), r ∈ H, r ≠ null ⊦ ¬ cyclic(r, H)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]