ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4145 on D77: Set 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. $\square$