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Proof step 63 from proof rem-stays-reachable-aux (previous step)

¬ x ≠ [], ce.nxt = H[H[(r ' + x).last].nxt].nxt, path(H[(r ' + x).last].nxt ' + x1 + 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, dups(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 64:
ce.nxt = H[H[r].nxt].nxt, path(H[r].nxt ' + x1 + H[r].nxt ', H), H[r].nxt ∈ H, r ∈ H ⊦ H[r].nxt = ce.nxt, H[r].nxt = null, 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);%e-01: ⊦ ¬ dups([]); from specification list-dup[reflist]%in-empty: ⊦ ¬ r ∈ []; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]