Bourbaki

Proposition 2

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

Theory of Sets, chapter II, § 3. Correspondences

Let G be a graph and let X, Y be two sets; then the relation X⊂YX \subset Y implies G⟨X⟩⊂G⟨Y⟩G\langle X \rangle \subset G\langle Y \rangle.

This is an immediate consequence of the definitions and of C50 (§ 1, no. 4).

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.

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Transcribed from the printed edition, 2004, Springer. Not translated.