----- > [!proposition] Proposition. ([[well-ordering of subsets]]) > If $A$ is a [[well-ordered set]], then any subset of $A$ [[well-ordered set|well-ordered]] in the restricted [[strict order relation]]. > [!proof]- Proof. ([[well-ordering of subsets]]) > Immediate from the definition. ----- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```