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Proof step 61 from proof rem-stays-reachable-aux (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
ce.nxt = H[H[(r ' + x).last].nxt].nxt, path(H[(r ' + x).last].nxt ' + x1 + H[(r ' + x).last].nxt ', H), path(r ' + x, H), (r ' + x).last ∈ H, H[(r ' + x).last].nxt ∈ H ⊦ H[(r ' + x).last].nxt = null, H[(r ' + x).last].nxt = ce.nxt, dups(x), (r ' + x).last ∈ x1, r ∈ x, ∃ x0. path(r ' + x0, H[(r ' + x).last, ce]) ∧ (r ' + x0).last = H[(r ' + x).last].nxt

Proof step 61 from proof rem-stays-reachable-aux (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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