
theorem RBProp:
  for fi being Fuzzy_Implication,
      x being Element of [.0,1.] holds
    fi.(x,1) = 1
  proof
    let fi be Fuzzy_Implication,
        x be Element of [.0,1.];
A1: fi.(1,1) = 1 by Def11;
B1: 1 in [.0,1.] by XXREAL_1:1;
    reconsider z = 1 as Element of [.0,1.] by XXREAL_1:1;
    x <= 1 by XXREAL_1:1; then
B2: fi.(1,1) <= fi.(x,1) by DefDecr,B1;
    fi.(x,z) in [.0,1.]; then
    fi.(x,1) <= 1 by XXREAL_1:1;
    hence thesis by XXREAL_0:1,A1,B2;
  end;
