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Proof step 53 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[(r ' + x).last].nxt].nxt, path(r ' + x, H), (r ' + x).last ∈ H, H[(r ' + x).last].nxt ∈ H, H[(r ' + x).last].nxt ≠ (r ' + x).last ∧ r = H[(r ' + x).last].nxt ∨ path(r ' + x0 + H[(r ' + x).last].nxt ', H) ∧ (r ' + x).last ≠ r ∧ ¬ (r ' + x).last ∈ x0 ∨ path(H[(r ' + x).last].nxt ' + x1 + H[(r ' + x).last].nxt ', H) ∧ ¬ (r ' + x).last ∈ x1 ⊦ H[(r ' + x).last].nxt = null, H[(r ' + x).last].nxt = ce.nxt, dups(x), r ∈ x, ∃ x0. path(r ' + x0, H[(r ' + x).last, ce]) ∧ (r ' + x0).last = H[(r ' + x).last].nxt

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 5

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