theorem Th13:
  FinJoin(B \/ {.b.},f) = FinJoin (B,f) "\/" f.b
proof
  set J= the L_join of 0L;
  thus FinJoin (B \/ {.b.},f) = J $$ (B \/ {.b.},f) by LATTICE2:def 3
    .= J $$ (B,f) "\/" f.b by SETWISEO:32
    .= FinJoin (B,f) "\/" f.b by LATTICE2:def 3;
end;
