theorem Th64:
  (the L_meet of L).(u, FinJoin(B, f)) = FinJoin(B, (the L_meet of L)[;](u,f))
proof
A1: (the L_meet of L).(u,Bottom L) = u"/\"Bottom L .= Bottom L;
  the L_meet of L is_distributive_wrt the L_join of L & Bottom L =
  the_unity_wrt the L_join of L by Th18,Th23;
  hence thesis by A1,SETWOP_2:12;
end;
