set IntRel = {} {{} },{{} };
for x being set st x in {{} } holds
not [x,x] in {} {{} },{{} } ;
then {} {{} },{{} } is_irreflexive_in {{} } by RELAT_2:def 2;
hence TrivAsymOrthoRelStr is irreflexive by Def12, CARD_1:87; :: thesis: verum