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Proof step 131 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 132:
H[H[r0].nxt].nxt = r0, H[r].nxt = H[r0].nxt, path(r0 ' + x + r ', H), r0 ∈ H, r ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = r0, r = H[r0].nxt, r = null, r0 = null, r0 = r, dups(x), r0 ∈ x, r ∈ x

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;%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)