 reserve a,b,c,x for Real;
 reserve C for non empty set;

theorem Glue:
  for f,g being PartFunc of REAL, REAL st
    f is continuous non empty &
    g is continuous non empty &
    (ex a,b,c being Real st dom f = [.a,b.] & dom g = [.b,c.]) &
    f tolerates g holds
      f +* g is continuous
  proof
    let f,g be PartFunc of REAL, REAL;
    assume f is continuous non empty & g is continuous non empty &
      (ex a,b,c being Real st dom f = [.a,b.] & dom g = [.b,c.]) &
      f tolerates g; then
    consider h being PartFunc of REAL, REAL such that
A2: h = f +* g & for x being Real st x in dom h holds h is_continuous_in x
      by LemGlue;
    thus thesis by A2;
  end;
