
theorem
  for fi being Fuzzy_Implication holds
    fi <= I_{1}
  proof
    let fi be Fuzzy_Implication;
    set f = I_{1};
    for x,y being Element of [.0,1.] holds
      f.(x,y) >= fi.(x,y)
    proof
      let x,y be Element of [.0,1.];
a0:   x <= 1 & y >= 0 by XXREAL_1:1;
      per cases;
      suppose
        x <> 1 or y <> 0; then
        x < 1 or y > 0 by a0,XXREAL_0:1; then
        f.(x,y) = 1 by I1Impl;
        hence thesis by XXREAL_1:1;
      end;
      suppose Aa: x = 1 & y = 0; then
        f.(x,y) = 0 by I1Impl;
        hence thesis by Aa,Def10;
      end;
    end;
    hence thesis by FUZNORM1:def 16;
  end;
