
theorem Th2:
  for L being antisymmetric RelStr, R being auxiliary(i) (Relation
of L), C being strict_chain of R, x, y being Element of L st x in C & y in C &
  x < y holds [x,y] in R
proof
  let L be antisymmetric RelStr, R be auxiliary(i) (Relation of L), C be
  strict_chain of R, x, y be Element of L;
  assume that
A1: x in C and
A2: y in C and
A3: x < y;
  [x,y] in R or [y,x] in R by A1,A2,A3,Def3;
  then [x,y] in R or y <= x by WAYBEL_4:def 3;
  hence thesis by A3,ORDERS_2:6;
end;
