reserve x,y,z for set;
reserve Q for left-distributive right-distributive complete Lattice-like non
  empty QuantaleStr,
  a, b, c, d for Element of Q;
reserve Q for Quantale,
  a,a9,b,b9,c,d,d1,d2,D for Element of Q;
reserve Q for Girard-Quantale,
  a,a1,a2,b,b1,b2,c,d for Element of Q,
  X for set;

theorem Th22:
  Bottom Bottom a = a
proof
  the absurd of Q is cyclic by Def19;
  then
A1: a-l>the absurd of Q = a-r>the absurd of Q;
  the absurd of Q is dualizing by Def20;
  hence thesis by A1;
end;
