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Proof step 57 from proof rem-stays-reachable-aux (previous step)

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, path(r ' + x0 + H[(r ' + x).last].nxt ', H[(r ' + x).last, ce]) ∧ (r ' + x0 + H[(r ' + x).last].nxt ').last = H[(r ' + x).last].nxt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
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, path(r ' + x0 + H[(r ' + x).last].nxt ', H[(r ' + x).last, ce])

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%last-01: ⊦ (r ' + x0 + r0 ').last = r0; from specification list-last[reflist]