
theorem LBProp:
  for fi being Fuzzy_Implication,
      y being Element of [.0,1.] holds
    fi.(0,y) = 1
  proof
    let fi be Fuzzy_Implication,
        y be Element of [.0,1.];
A1: fi.(0,0) = 1 by Def00;
B1: 0 in [.0,1.] by XXREAL_1:1;
    reconsider z = 0 as Element of [.0,1.] by XXREAL_1:1;
    0 <= y by XXREAL_1:1; then
B2: fi.(0,0) <= fi.(0,y) by DefIncr,B1;
    fi.(z,y) in [.0,1.]; then
    fi.(0,y) <= 1 by XXREAL_1:1;
    hence thesis by XXREAL_0:1,A1,B2;
  end;
