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Proof step 13 from proof rem-stays-reachable-aux (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
(r ' + x0).last = H[r].nxt, ce.nxt = H[H[r].nxt].nxt, path(r ' + x0, H[r, ce]), H[r].nxt ∈ H, r ∈ H, H[r].nxt ∈ H[r, ce] ⊦ H[r].nxt = ce.nxt, H[r].nxt = null, r = null, dups(x0), r ∈ x0, ∃ x. path(H[r].nxt ' + x + H[r].nxt ', H) ∧ ¬ r ∈ x

Rule argument

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ r ∈ H ∧ r ≠ null;% ⊦ ¬ dups([]); (s)% ⊦ ¬ r ∈ []; (s)% ⊦ r '.last = r; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + [] = x0; (s)