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Proof step 134 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule constructor cut

And closed the goal!

Rule argument

var: x0

Additional information

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