reserve x,X,Y for set;
reserve C for non empty set;
reserve c for Element of C;
reserve V for RealNormSpace;
reserve f,f1,f2,f3 for PartFunc of C,V;
reserve r,r1,r2,p for Real;

theorem
  for f1 be PartFunc of C,REAL holds f1 is total & f2 is total implies
  (f1(#)f2)/.c = f1.c * (f2/.c)
proof
  let f1 be PartFunc of C,REAL;
  assume f1 is total & f2 is total;
  then dom (f1(#)f2) = C by PARTFUN1:def 2;
  hence thesis by Def3;
end;
