
theorem lemtrans:
for X being non empty set
for R being transitive Relation of X
for x,y,z being Element of X st x <=_R,y & y <=_R,z holds x <=_R,z
proof
let X be non empty set; let R be transitive Relation of X;
let x,y,z be Element of X;
assume A: x <=_R,y & y <=_R,z;
then x in field R & y in field R & z in field R by RELAT_1:15;
hence thesis by A,RELAT_2:def 8,RELAT_2:def 16;
end;
