reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;
reserve A,B for set;
reserve x,y,i,j,k for object;

theorem Th102:
 for x being object holds
  f+~(x,x) = f
proof let x be object;
  thus f+~(x,x) = f+*((id{x})*f) by Th96
    .= f by Th98,RELAT_1:50;
end;
