
theorem Prop136c: :: Proposition 1.3.6 c) p. 13
  for I being Fuzzy_Implication,
      f being bijective increasing UnOp of [.0,1.] st
   I is satisfying_(IP) holds
   ConjImpl (I,f) is satisfying_(IP)
  proof
    let I be Fuzzy_Implication,
        f be bijective increasing UnOp of [.0,1.];
    assume
B0: I is satisfying_(IP);
    set g = ConjImpl (I,f);
    let x be Element of [.0,1.];
    g.(x,x) = f".(I.(f.x,f.x)) by BIDef
           .= f".1 by FUZIMPL2:def 3,B0
           .= 1 by LemmaBound;
    hence thesis;
  end;
