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Proof step 55 from proof rem-stays-reachable-aux (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
ce.nxt = H[H[(r ' + x).last].nxt].nxt, path(r ' + x0 + H[(r ' + x).last].nxt ', H), path(r ' + x, H), H[(r ' + x).last].nxt ∈ H, (r ' + x).last ∈ H ⊦ H[(r ' + x).last].nxt = ce.nxt, H[(r ' + x).last].nxt = null, (r ' + x).last = r, r ∈ x, dups(x), (r ' + x).last ∈ x0, ∃ x0. path(r ' + x0, H[(r ' + x).last, ce]) ∧ (r ' + x0).last = H[(r ' + x).last].nxt

Proof step 55 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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