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 Th38:
  a [= b implies for a9,b9 being Element of L.: st a = a9 & b = b9
  holds b9 [= a9
proof
  assume a [= b;
  then
A1: a "\/" b = b;
  let a9,b9 be Element of L.:;
  assume a = a9 & b = b9;
  then b9 "/\" a9 = b9 by A1,Th37;
  hence thesis by LATTICES:4;
end;
