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Proof step 9 from proof pathex-def-nodups (previous step)

list2set(refs0) ∩ list2set(refs) = ∅, validrefs(str, r ' + refs0 + r ' + refs, st[r -- _type] .type, st), validrefs(str, r ' + refs, st[r -- _type] .type, st) ⊦ r = (r ' + refs) .last, r ∈ refs, r ∈ refs0, dups(refs), dups(refs0), ∃ refs1. refs1 ≠ [] ∧ refs1 .first = r ∧ refs1 .last = (refs1 .first ' + refs) .last ∧ ¬ dups(refs1) ∧ validrefs(str, refs1, st[refs1 .first -- _type] .type, st)

User applied rule exists right

And closed the goal!

Rule argument

[EXRARG : pos: right 6, [extquanttermlist: (r ' + refs) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ r ∈ refs → (dups(r ' + refs) ↔ dups(refs))])], [EXTRATERMS : (r ' + refs)]]