
theorem lemanti:
for X being non empty set
for R being antisymmetric Relation of X
for x,y being Element of X st x <=_R,y & y <=_R,x holds x = y
proof
let X be non empty set; let R be antisymmetric Relation of X;
let x,y be Element of X;
assume A: x <=_R,y & y <=_R,x;
then x in field R & y in field R by RELAT_1:15;
hence x = y by A,RELAT_2:def 4,RELAT_2:def 12;
end;
