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

Result R4145 on D77: Set union
Subresult of R4144: Finite union is an upper bound to each set in the union

Binary union is an upper bound to both sets in the union

Formulation 0

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

(i)	$A \cup B$ is the D77: Set union of $A$ and $B$

Then

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

Proofs

Proof 0

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

(i)	$A \cup B$ is the D77: Set union of $A$ and $B$

This result is a particular case of R4144: Finite union is an upper bound to each set in the union. $\square$