ThmDex – An index of mathematical definitions, results, and conjectures.

Result R4151 on D76: Set intersection
Subresult of R4150: Finite intersection is a lower bound to each set in the intersection

Binary intersection is a lower bound to each set in the intersection

Formulation 0

Let $A$ and $B$ each be a D11: Set such that

(i)	$A \cap B$ is the D76: Set intersection of $A$ and $B$

Then

(1)	\begin{equation} A \cap B \subseteq A \end{equation}
(2)	\begin{equation} A \cap B \subseteq B \end{equation}

Also known as

Binary set intersection is a subset of both sets in the intersection

Proofs

Proof 0

Let $A$ and $B$ each be a D11: Set such that

(i)	$A \cap B$ is the D76: Set intersection of $A$ and $B$