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

H[(r ' + x).last].nxt ≠ (r ' + x).last ∧ r = H[(r ' + x).last].nxt, 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 54:
r = H[(r ' + x).last].nxt, ce.nxt = H[r].nxt, path(r ' + x, H), r ∈ H, (r ' + x).last ∈ H ⊦ r = ce.nxt, r = null, r = (r ' + x).last, r ∈ x, dups(x), ∃ x0. path(r ' + x0, H[(r ' + x).last, ce]) ∧ (r ' + x0).last = r

Proof step 53 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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