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Proof step 5 from proof reachable-n-rec2 (previous step)

⊦ (∃ r1. reachable-1(H, r, r1) ∧ reachable-1(H, r1, r0)) ↔ reachable-1(H, r, H[r].nxt) ∧ reachable-1(H, H[r].nxt, r0)

User applied rule case distinction

And obtained the following new goals

Proof step 6:
reachable-1(H, r, H[r].nxt) ∧ reachable-1(H, H[r].nxt, r0) ⊦ ∃ r1. reachable-1(H, r, r1) ∧ reachable-1(H, r1, r0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: reachable-1-def: ⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0;