| cyclic(str, r, st), unchanged(str, r, st, st0) ⊦ junkref(str, r, st), ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st0[refs .first -- _type] .type, st0) |
⊦ cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st))
∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st), unchanged(str, r, st, st0) ⊦ junkref(str, r, st), ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st0[refs .first -- _type] .type, st0)
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, str)]]