reserve n for non zero Element of NAT;
reserve a,b,r,t for Real;

theorem
  for X be non empty closed_interval Subset of REAL,Y be RealNormSpace,
      f be continuous PartFunc of REAL,Y
    st dom f=X holds modetrans(f,X,Y)=f
proof
  let X be non empty closed_interval Subset of REAL,Y be RealNormSpace,
  f be continuous PartFunc of REAL,Y;
  assume dom f = X; then
  f in ContinuousFunctions(X,Y) by Def2;
  hence thesis by Def5;
end;
