= Quotient vector bundle
{title2=$E/F$}
For a smooth <vector subbundle> $F\subset E$, the quotient has <fibers> $(E/F)_p=E_p/F_p$. Extend a local <frame of a vector bundle> of $F$ to one of $E$; the classes of the complementary frame vectors trivialize the quotient. Adapted <transition functions of a vector bundle> are block upper triangular, and their lower-right blocks give the quotient transitions. These are smooth and satisfy the cocycle identity, defining a smooth <vector bundle>. The projection $E\to E/F$ is a smooth <vector bundle morphism>.
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