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 V being scalar-unital non empty RLSStruct
  for f being PartFunc of C,V holds
  1(#)f = f
proof
  let V be scalar-unital non empty RLSStruct;
  let f be PartFunc of C,V;
A1: now
    let c;
    assume c in dom (1(#)f);
    hence (1(#)f)/.c = 1 * f/.c by Def4
      .= f/.c by RLVECT_1:def 8;
  end;
  dom (1(#)f) = dom f by Def4;
  hence thesis by A1,PARTFUN2:1;
end;
