reserve a,b,c,d,e,x,r for Real,
  A for non empty closed_interval Subset of REAL,
  f,g for PartFunc of REAL,REAL;

theorem Th3:
  for R be Relation, A,B,C be set st A c= B & A c= C holds (R|B)|A
  = (R|C)|A
proof
  let R be Relation, A,B,C be set;
  assume that
A1: A c= B and
A2: A c= C;
  (R|C)|A = R|A by A2,RELAT_1:74;
  hence thesis by A1,RELAT_1:74;
end;
