Proof step 1 from proof rem-stays-reachable-aux2 (conclusion)

User applied rule case distinction

And obtained the following new goals

• Proof step 2:

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

• Proof step 18:

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

Rule argument

Additional information