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Theorems · Theorem · group theory

AddLocalization.mk_left_injective

∀ {α : Type u_1} [inst : AddCommMonoid α] [IsCancelAdd α] {s : AddSubmonoid α} (b : ↥s),
  Function.Injective fun a => AddLocalization.mk a b
Defined in
Mathlib.GroupTheory.MonoidLocalization.Basic
Cited by
1 results in Mathlib
Foundations
Depth 54 from the axioms · uses propext, Quot.sound
Assumes
AddCommMonoidIsCancelAdd
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Around this declaration

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

AffineAddMonoid.embedding_injective · cited by 0AffineAddMonoid.embedding…AddCommMonoid · cited by 12281AddCommMonoidAddSubmonoid · cited by 1178AddSubmonoidIsCancelAdd · cited by 79IsCancelAddadd_right_inj · cited by 71add_right_injAddLocalization · cited by 38AddLocalizationAddLocalization.mk · cited by 28AddLocalization.mkAddLocalization.mk_eq_mk_iff · cited by 5AddLocalization.mk_eq_mk_…AddLocalization.r_iff_exists · cited by 5AddLocalization.r_iff_exi…AddLocalization.mk_left_injec…CITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.