Exercise Show that $[0,1]$ possesses the infinite distributive law, i.e. show that finite meets distribute over arbitrary joins.
Distributive law: $a \land(\bigvee_{i \in I} b_i) = \bigvee_{i \in I} (a \land b_i)$
I understand that the unit interval $[0,1]$ is a complete lattice, since it is closed under both arbitrary joins and meets. How should one go about proving this point, however?
Any comments or advice on this issue is greatly appreciated in advance.