
theorem NormIn01:
  for a,b being Real,
      t being BinOp of [.0,1.] holds
   t.(a,b) in [.0,1.]
  proof
    let a,b be Real;
    let t be BinOp of [.0,1.];
    per cases;
    suppose a in [.0,1.] & b in [.0,1.]; then
      [a,b] in [:[.0,1.], [.0,1.]:] by ZFMISC_1:87;
      hence thesis by FUNCT_2:5;
    end;
    suppose not a in [.0,1.] or not b in [.0,1.]; then
      not [a,b] in dom t by ZFMISC_1:87; then
      t. [a,b] = 0 by FUNCT_1:def 2;
      hence thesis by XXREAL_1:1;
    end;
  end;
