Corollary 3

Tag 03RE, permanent. Cite it as [Bourbaki, Tag 03RE].

Theory of Sets, chapter III, § 4. Natural integers. Finite sets

If $f$ is a mapping of a finite set E into a set F, then $f(\mathrm{E})$ is a finite subset of F.

For $\mathrm{Card}\ (f(\mathrm{E})) \leqslant \mathrm{Card}\ (\mathrm{E})$ (§ 3, no. 2, Proposition 3).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

alg--s0 not in this corpus
Corollary 1, § 5

Cites

§ 3, no. 2, Proposition 3