reserve Y for non empty set,
  a for Function of Y,BOOLEAN,
  G for Subset of PARTITIONS(Y),
  P,Q for a_partition of Y;

theorem Th7:
  for R,S being Relation, Y being set st R is_reflexive_in Y &
  S is_reflexive_in Y holds R*S is_reflexive_in Y
proof
  let R,S be Relation, Y be set such that
A1: R is_reflexive_in Y & S is_reflexive_in Y;
  let x be object;
  assume x in Y;
  then [x,x] in R & [x,x] in S by A1;
  hence thesis by RELAT_1:def 8;
end;
