::> :: clusters constructors definition definitions notation notations registration registrations requirements scheme schemes signature theorem theorems vocabularies case end hereby now proof suppose for ex not & or implies iff st holds being assume cases given hence let per take thus and antonym attr as be begin canceled cluster coherence compatibility consistency contradiction correctness def deffunc defpred environ equals existence func if irreflexivity it means mode of otherwise over pred provided qua reconsider redefine reflexivity reserve struct such synonym that thesis where associativity commutativity connectedness irreflexivity reflexivity symmetry uniqueness transitivity idempotence asymmetry projectivity involutiveness by