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Proof step 2 from proof reachable-split-last (previous step)

⊦ r = r0, reachable(r, r0, H) ↔ (∃ r1. reachable(r, r1, H) ∧ H[r1].nxt = r0 ∧ H[r1].nxt ∈ H ∧ H[r1].nxt ≠ null)

User applied rule case distinction

And obtained the following new goals

Proof step 3:
reachable(r, r0, H) ⊦ ∃ r1. reachable(r, r1, H) ∧ H[r1].nxt = r0 ∧ H[r1].nxt ∈ H ∧ H[r1].nxt ≠ null, r = r0

Rule argument

pos: right 2

Additional information

Used simplifier rules: reach-reachnext: ⊦ reachable(r, r1, H) → (¬ reachable(r, H[r1].nxt, H) ↔ H[r1].nxt = null ∨ ¬ H[r1].nxt ∈ H);