Union


THEOREM   

Union is idempotent.

Proof available

THEOREM   

Union is commutative.

Proof available

THEOREM   

Union is associative.

Proof available

LEMMA   

Union is left self-distributive.

$$A \cup (B \cup C) = (A \cup B) \cup (A \cup C)$$

Proof available

LEMMA   

Union is right self-distributive.

$$(B \cup C) \cup A = (B \cup A) \cup (C \cup A)$$

Proof available

THEOREM   

Union is self-distributive.

Proof available