
theorem Prop136a: :: Proposition 1.3.6 a) p. 13
  for I being Fuzzy_Implication,
      f being bijective increasing UnOp of [.0,1.] st
   I is satisfying_(NP) holds
   ConjImpl (I,f) is satisfying_(NP)
  proof
    let I be Fuzzy_Implication,
        f be bijective increasing UnOp of [.0,1.];
    assume
B0: I is satisfying_(NP);
    set g = ConjImpl (I,f);
A0: 1 in [.0,1.] by XXREAL_1:1;
    let y be Element of [.0,1.];
    g.(1,y) = f".(I.(f.1, f.y)) by A0,BIDef
           .= f".(I.(1,f.y)) by LemmaBound
           .= f".(f.y) by B0,FUZIMPL2:def 1;
    hence thesis by FUNCT_2:26;
  end;
