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Proof step 3 from proof pathex-def-nodups (previous step)

refs .last = refs1 .last, validrefs(str, refs .first ' + refs1, st[refs .first -- _type] .type, st), dups(refs1), validrefs(str, refs, st[refs .first -- _type] .type, st) ⊦ refs = [], refs .first = refs1 .last, refs1 = [], dups(refs), ∃ refs0. refs0 ≠ [] ∧ refs0 .first = refs .first ∧ refs0 .last = refs1 .last ∧ ¬ dups(refs0) ∧ validrefs(str, refs0, st[refs0 .first -- _type] .type, st)

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

[EXRARG : pos: right 5, [QUANTTERMLIST : (refs)]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refs)]]