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
  FinJoin(B,f) [= u implies for x st x in B holds f.x [= u
proof
  assume
A1: FinJoin(B,f) [= u;
  let x;
  assume x in B;
  then f.x [= FinJoin(B,f) by Th28;
  hence thesis by A1,LATTICES:7;
end;
