Injection


Definition

Let \(f : A \longrightarrow B\) be a function from \(A\) to \(B\). Then \(f : A \longrightarrow B\) is injective if and only if

$$\forall x,y \in A : f(x) = f(y) \Rightarrow x = y$$
Fun.inj_def: inj ?f = (\(\forall\)x y. ?f x = ?f y \(\longrightarrow\) x = y)
THEOREM    The composition of two injective functions is injective.

Proof available

Proper subsets