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Proof step 20 from proof cyclic-def-shortest (previous step)

validrefs(str, (r ' + refs1) + r0 ', st[r -- _type] .type, st) ⊦ dups(refs1), r ∈ refs1, ∃ refs0. dups(refs0) ∧ refs0 .first = r ∧ validrefs(str, refs0, st[refs0 .first -- _type] .type, st), r0 ≠ r ∧ ¬ r0 ∈ refs1

User applied rule exists right

And closed the goal!

Rule argument

[EXRARG : pos: right 3, [extquanttermlist: ((r ' + refs1) + r0 ') abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs], [CSIMPSEQ : ⊦ dups(refs + r ') ↔ r ∈ refs ∨ dups(refs)], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ (r ' + refs) .first = r])], [EXTRATERMS : ((r ' + refs1) + r0 ')]]