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Proof step 48 from proof acyclic-rem-not-reachable (previous step)

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

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 10 terms: x + H[r].nxt '

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%last-01: ⊦ (r ' + x0 + r0 ').last = r0; from specification list-last[reflist] Used terms: x + H[r].nxt '