reserve X for set, R,R1,R2 for Relation;
reserve x,y,z for set;
reserve n,m,k for Nat;

theorem
  for X being non empty set
  for R being total connected Relation of X
  for x,y being Element of X st x <> y holds x,y in R or y,x in R
  proof
    let X be non empty set;
    let R be total connected Relation of X;
    let x,y be Element of X;
    field R = X by ORDERS_1:12; then
    x <> y implies [x,y] in R or [y,x] in R by RELAT_2:def 6,def 14;
    hence thesis;
  end;
