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Proof step 64 from proof rem-stays-reachable-aux2 (previous step)

r0 = H[r0].nxt, r1 ∈ H, path(r0 ' + x1 + r1 ', H), r0 ∈ H, path(r ' + (x2 + r1 ') + r0 ', H), path(r ' + x + r1 ', H) ⊦ r0 = r, r0 = null, r = r1, r0 = r1, r0 ∈ x2, r1 ∈ x2, dups(x2), r ∈ x2, r1 ∈ x, dups(x), r ∈ x, r1 ∈ x1, dups(x1), r0 ∈ x1

User applied rule constructor cut

And closed the goal!

Rule argument

var: x1

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]%rec: ⊦ dups(r ' + x0) ↔ ¬ ¬(r ∈ x0 ∨ dups(x0)); from specification list-dup[reflist]%Nil: ⊦ [] + x0 = x0; from specification list[reflist]