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;

theorem Th9:
  a [= b & c [= d implies a [*] c [= b [*] d
proof
  assume a [= b & c [= d;
  then a [*] c [= b [*] c & b [*] c [= b [*] d by Th8;
  hence thesis by LATTICES:7;
end;
