
theorem ConormIs1:
  for t being commutative monotonic with-0-identity BinOp of [.0,1.] holds
    for a being Element of [.0,1.] holds
      t.(a,1) = 1
  proof
    let t be commutative monotonic with-0-identity BinOp of [.0,1.];
    let a be Element of [.0,1.];
T0: 0 in [.0,1.] & 1 in [.0,1.] by XXREAL_1:1; then
T3: t.(0,1) = t.(1,0) by BINOP_1:def 2 .= 1 by T0,ZeroDef;
    for a being Element of [.0,1.] holds t.(a,1) = 1
    proof
      let a be Element of [.0,1.];
      t.(a,1) in [.0,1.] by NormIn01; then
T4:   t.(a,1) <= 1 by XXREAL_1:1;
      0 <= a by XXREAL_1:1; then
      1 <= t.(a,1) by T0,MonDef,T3;
      hence thesis by XXREAL_0:1,T4;
    end;
    hence thesis;
  end;
