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Proof step 1 from proof reachable-addnew-rev (conclusion)

⊦ ¬ r2 ∈ H ∧ r ∈ H ∧ ¬ reachable(r, r1, H) → (reachable(r, r1, H[r2, ce]) ↔ (∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ r2 ≠ null ∧ (r1 = r2 ∨ reachable(ce.nxt, r1, H))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
r ∈ H ⊦ reachable(r, r1, H[r2, ce]) ↔ (∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ (r1 = H[r0].nxt ∨ reachable(ce.nxt, r1, H))), reachable(r, r1, H), r2 ∈ H

Proof step 1 from proof reachable-addnew-rev (conclusion)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information