reserve L for Lattice;
reserve X,Y,Z,V for Element of L;

theorem
  X "\/" Y [= Z implies X [= Z
proof
  assume X "\/" Y [= Z;
  then X "/\" (X "\/" Y) [= X "/\" Z by LATTICES:9;
  then
A1: X [= X "/\" Z by LATTICES:def 9;
  X "/\" Z [= Z by LATTICES:6;
  hence thesis by A1,LATTICES:7;
end;
