theorem Th23:
  FinMeet B1 "/\" FinMeet B2 = FinMeet (B1 \/ B2)
proof
  set M = the L_meet of 1L;
  thus FinMeet (B1 \/ B2) = M $$ (B1 \/ B2,id 1L) by LATTICE2:def 4
    .= M $$ (B1,id 1L) "/\" M $$ (B2,id 1L) by SETWISEO:33
    .= FinMeet B1 "/\" M $$ (B2,id 1L) by LATTICE2:def 4
    .=FinMeet B1 "/\" FinMeet B2 by LATTICE2:def 4;
end;
