reserve x,y,X,X1,Y,Z for set;
reserve L for Lattice;
reserve F,H for Filter of L;
reserve p,q,r for Element of L;
reserve L1, L2 for Lattice;
reserve a1,b1 for Element of L1;
reserve a2 for Element of L2;
reserve f for Homomorphism of L1,L2;
reserve B for Element of Fin the carrier of L;

theorem Th9:
  FinJoin {.p.} = p
proof
  thus FinJoin {.p.} =(the L_join of L) $$ ({.p.},id L) by LATTICE2:def 3
    .= (id L).p by SETWISEO:17
    .= p by FUNCT_1:18;
end;
