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Proof step 19 from proof reachable-nodups-def (previous step)

(r ' + x1).last = (H[r].nxt ' + x0).last, path(H[r].nxt ' + x0, H), r ∈ H, path(H[r].nxt ' + x2 + r ' + x1, H), ∀ r, H. path(r ' + x0, H) → (∃ x1. path(r ' + x1, H) ∧ (r ' + x1).last = (r ' + x0).last ∧ ¬ r ∈ x1 ∧ ¬ dups(x1)) ⊦ r = null, r = H[r].nxt, r ∈ x1, r ∈ x2, dups(x2 + x1), H[r].nxt ∈ x2, H[r].nxt ∈ x1, dups(x2), dups(x1), ∃ x. path(r ' + x, H) ∧ (r ' + x).last = (r ' + x1).last ∧ ¬ r ∈ x ∧ ¬ dups(x)

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 10 terms: x1

Additional information

Used simplifier rules: path-postfix: ⊦ path(x + r ' + y, H) → (¬ path(r ' + y, H) ↔ false);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used terms: x1