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Proof step 45 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
(H[r].nxt ' + x0).last = r, H[r].nxt = H[H[r].nxt].nxt, path(H[r].nxt ' + x0, H), H[r].nxt ∈ H, r ∈ H ⊦ H[r].nxt = r, H[r].nxt = null, r = null, dups(x0), H[r].nxt ∈ x0

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)