Proof step 2 from proof rem-stays-reachable-aux2 (previous step)

User applied rule case distinction

And obtained the following new goals

• Proof step 3:

  reachable(r, r0, H), H[r0].nxt ∈ H, ∃ r1. reachable(r, r1, H) ∧ H[r0].nxt = H[r1].nxt ∧ ¬ reachable(r0, r1, H) ⊦ H[r0].nxt = null, ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ r0 ≠ r ∧ ¬ r0 ∈ x

• Proof step 19:

  reachable(r, r0, H), H[r0].nxt ∈ H, ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ r0 ≠ r ∧ ¬ r0 ∈ x ⊦ H[r0].nxt = null, ∃ r1. reachable(r, r1, H) ∧ H[r0].nxt = H[r1].nxt ∧ ¬ reachable(r0, r1, H)

Rule argument

Additional information