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Proof step 11 from proof cyclic-subset-01 (previous step)

st ⊆ st0, validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ junkref(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0), ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st0[refs .first -- _type] .type, st0)

User applied rule exists right

And obtained the following new goals

Proof step 10:
st ⊆ st0, validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ junkref(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0), dups(r ' + refs0) ∧ (r ' + refs0) .first = r ∧ validrefs(str, r ' + refs0, st0[(r ' + refs0) .first -- _type] .type, st0)

Rule argument

[EXRARG : pos: right 3, [extquanttermlist: (r ' + refs0) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r ' + refs0)]]