----- > [!proposition] Proposition. ([[cancellation law for groups]]) > Let $a,b,c$ be elements of a [[group]] $G$ whose [[binary operation]] is written multiplicatively. If $ab=ac$ or if $ba=ca$, then $b=c$. If $ab=a$ or if $ba=a$, then $b=1$. > [!proof]- Proof. ([[cancellation law for groups]]) > Left-multiply both sidees of $ab=ac$ by $a^{-1}$ to obtain $b=c$, etc. ----- #### ---- #### 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 > ```