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Proof step 42 from proof rem-stays-reachable-aux2 (previous step)

(r ' + x1).last = (r ' + x).last, (r0 ' + x0).last = (r ' + x).last, r0 = H[r0].nxt, x = [], path(r ' + x1, H), path(r0 ' + x0, H), path(r ' + x + r0 ', H), r0 ∈ H, (r ' + x).last ∈ H ⊦ r0 = r, r0 = null, dups(x0), dups(x1), dups(x), r0 ∈ x, r0 ∈ x0, r ∈ x1, r ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
(r ' + x1).last = r, (H[r].nxt ' + x0).last = r, H[r].nxt = H[H[r].nxt].nxt, path(r ' + x1, H), path(H[r].nxt ' + x0, H), H[r].nxt ∈ H, r ∈ H ⊦ H[r].nxt = r, H[r].nxt = null, r = null, dups(x0), dups(x1), H[r].nxt ∈ x0, r ∈ x1

Rule argument

Additional information

Used simplifier rules: path-two: ⊦ path(r ' + r0 ', H) ↔ r ∈ H ∧ r0 ∈ H ∧ r ≠ null ∧ r0 ≠ null ∧ H[r].nxt = r0;% ⊦ ¬ dups([]); (s)% ⊦ ¬ r ∈ []; (s)% ⊦ r '.last = r; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + [] = x0; (s)