Library functional_algebra.function

This module defines basic properties for functions.
Copyright (C) 2018 Larry D. Lee Jr. <llee454@gmail.com>
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Defines the injective predicate.
Definition is_injective (A B : Type) (f : A -> B) : Prop
  := forall x y : A, f x = f y -> x = y.

Defines the onto predicate.
Definition is_onto (A B : Type) (f : A -> B) : Prop
  := forall y : B, exists x : A, f x = y.

Defines the bijective predicate.
Definition is_bijective (A B : Type) (f : A -> B) : Prop
  := is_injective A B f /\ is_onto A B f.