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
  f is total implies (r(#)f)/.c = r * (f/.c)
proof
  assume f is total;
  then dom (r(#)f) = C by PARTFUN1:def 2;
  hence thesis by Def4;
end;
