for A, O being non empty set
for R being Order of A
for Ol being Equivalence_Relation of O
for f being Function of O,(A *)
for g being Function of O,A holds
( not OverloadedRSSign(# A,R,O,Ol,f,g #) is empty & not OverloadedRSSign(# A,R,O,Ol,f,g #) is void & OverloadedRSSign(# A,R,O,Ol,f,g #) is reflexive & OverloadedRSSign(# A,R,O,Ol,f,g #) is transitive & OverloadedRSSign(# A,R,O,Ol,f,g #) is antisymmetric )