reserve X,Y,Z,x,y,z for set;
reserve T,R for Tolerance of X;

theorem Th7:
 for x being object holds
  for T being total reflexive Relation of X holds x in X iff [x,x] in T
proof let x be object;
  let T be total reflexive Relation of X;
  thus x in X implies [x,x] in T by EQREL_1:5;
  assume
A1: [x,x] in T;
  field T = X by ORDERS_1:12;
  hence thesis by A1,RELAT_1:15;
end;
