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Proof step 50 from proof rem-stays-reachable-aux2 (previous step)

H[r].nxt = H[H[r].nxt].nxt, H[r].nxt ∈ H, path(H[r].nxt ' + x + r ', H), r ∈ H ⊦ r = null, H[r].nxt = null, H[r].nxt = r, H[r].nxt ∈ x, r ∈ x, dups(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 [], +;;%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]%in-empty: ⊦ ¬ r ∈ []; from specification list[reflist]%e-01: ⊦ ¬ dups([]); from specification list-dup[reflist]