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Proof step 64 from proof rem-stays-reachable-aux (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 65:
ce.nxt = H[H[r].nxt].nxt, path(H[r].nxt ' + x1 + H[r].nxt ', H), r ∈ H, H[r].nxt ∈ H ⊦ H[r].nxt = null, H[r].nxt = ce.nxt, r = null, r ∈ x1, ∃ x. path(r ' + x, H[r, ce]) ∧ (r ' + x).last = H[r].nxt

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)