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
  a delta b delta c = a delta (b delta c)
proof
  thus a delta b delta c = Bottom (Bottom a [*] Bottom b [*] Bottom c) by Th22
    .= Bottom (Bottom a [*] (Bottom b [*] Bottom c)) by GROUP_1:def 3
    .= a delta (b delta c) by Th22;
end;
