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Proof step 51 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule constructor cut

And closed the goal!

Rule argument

var: x

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)% ⊦ ¬ r ∈ []; (s)% ⊦ ¬ dups([]); (s)