 reserve X,a,b,c,x,y,z,t for set;
 reserve R for Relation;

theorem Pom2:
  for R1, R2 being non empty RelStr,
      X being Subset of R1,
      Y being Subset of R2 st
    the RelStr of R1 = the RelStr of R2 & X = Y holds
      LAp X = LAp Y
  proof
    let R1, R2 be non empty RelStr,
        X be Subset of R1,
        Y be Subset of R2;
    assume that
A1: the RelStr of R1 = the RelStr of R2 and
A2: X = Y;
    LAp X = { x where x is Element of R1 :
      Class (the InternalRel of R1, x) c= X } by ROUGHS_1:def 4
      .= LAp Y by A1,A2,ROUGHS_1:def 4;
    hence thesis;
  end;
