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Theorems · Definition · order theory

Localization.mkOrderEmbedding

{α : Type u_1} →
  [inst : CommMonoid α] →
    [inst_1 : PartialOrder α] → [inst_2 : IsOrderedCancelMonoid α] → {s : Submonoid α} → ↥s → α ↪o Localization s

An ordered cancellative monoid injects into its localization by sending a to a / b.

Defined in
Mathlib.GroupTheory.MonoidLocalization.Order
Cited by
1 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidPartialOrderIsOrderedCancelMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Localization.mkOrderEmbedding_apply · cited by 0Localization.mkOrderEmbed…PartialOrder · cited by 6410PartialOrderSubmonoid · cited by 3086SubmonoidCommMonoid · cited by 2264CommMonoidOrderEmbedding · cited by 619OrderEmbeddingLocalization · cited by 270LocalizationLocalization.mk · cited by 110Localization.mkIsOrderedCancelMonoid · cited by 65IsOrderedCancelMonoidLocalization.mkOrderEmbeddingCITED BYCITES

Cites7

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Cited by1

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