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Proof step 133 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), r0 ∈ H, H[r0].nxt ∈ H, r ∈ H ⊦ r = null, r0 = null, H[r0].nxt = r0, r = H[r0].nxt, r0 = r, H[r0].nxt = null, r ∈ x0, r0 ∈ x0, dups(x0), H[r0].nxt ∈ 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 [], +;;%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%in-06: ⊦ ¬ r ∈ r0 ' + x0 ↔ r ≠ r0 ∧ ¬ r ∈ x0; from specification list[reflist]%Nil: ⊦ [] + x0 = x0; from specification list[reflist]