Bourbaki

Corollary 2

Tag 06X9, permanent. Cite it as [Bourbaki, Tag 06X9].

Algebra, chapter VI, § 1. Ordered groups. Divisibility

— In a lattice ordered group, if x and y are coprime and if z ≥0\geq 0 and x≤y+zx \leq y + z, then x≤zx \leq z.

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

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Cites

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Transcribed from the printed edition, 2003, Springer. Not translated.