Intersection


THEOREM   

Intersection is idempotent.

$$A \cap A = A$$

Proof available

THEOREM   

Intersection is commutative.

$$A \cap B = B \cap A$$

Proof available

THEOREM   

Intersection is associative.

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

Proof available

LEMMA   

Intersection is left self-distributive.

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

Proof available

LEMMA   

Intersection is right self-distributive.

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

Proof available

THEOREM   

Intersection is self-distributive.

Proof available