theorem Th19:
  the L_meet of L is having_a_unity implies Top L = the_unity_wrt
  the L_meet of L
proof
  set J = the L_meet of L;
  given u such that
A1: u is_a_unity_wrt J;
  (the L_meet of L).(u,v) = v by A1,BINOP_1:4;
  then u = Top L by Th17;
  hence thesis by A1,BINOP_1:def 8;
end;
