reserve A for set,
  C for non empty set,
  B for Subset of A,
  x for Element of A,
  f,g for Function of A,C;
reserve B for Element of Fin A;
reserve L for non empty LattStr,
  a,b,c for Element of L;
reserve L for Lattice;
reserve a,b,c,u,v for Element of L;
reserve A for non empty set,
  x for Element of A,
  B for Element of Fin A,
  f,g for Function of A, the carrier of L;

theorem Th39:
  for a9,b9 being Element of L.: st a9 [= b9 & a = a9 & b = b9 holds b [= a
proof
  let a9,b9 be Element of L.:;
  assume that
A1: a9 [= b9 and
A2: a = a9 & b = b9;
  a9 "\/" b9 = b9 by A1;
  then b "/\" a = b by A2,Th37;
  hence thesis by LATTICES:4;
end;
