Definition 5

Tag 055H, permanent. Cite it as [Bourbaki, Tag 055H].

A law of composition $(x, y) \mapsto x \top y$ on a set E is called associative if, for all elements $x, y, z$ in E,

(x \top y) \top z = x \top (y \top z).

A magma whose law is associative is called an associative magma.

The opposite law of an associative law is associative.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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