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Proof step 3 from proof reachable-split-last (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 4:
reachable(r, r0, H) ⊦ r = r0, ∃ r1. reachable(r, r1, H) ∧ H[r1].nxt = r0 ∧ H[r1].nxt ∈ H ∧ H[r1].nxt ≠ null

Rule argument

pos: right 1

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));