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State/Bijections are injective and surjective functions
Proposition: (Bijections are injective and surjective functions) Suppose that $X$ and $Y$ are sets, and $f \colon X \rightarrow Y$ is a function. Then $f$ is a bijection if and only if $f$ is both injective and surjective.
This statement logically relies on the following definitions and statements: Def/Bijection, Def/Injective, Def/Surjective, State/Injective functions have left inverses, State/Surjective functions have right inverses, Def/Composite function
The following statements and definitions rely on the material of this page: State/Composing injective surjective or bijective functions yields the same
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