Theorems · Theorem · commutative algebra
Module.Invertible.bijective
∀ {R : Type u} {M : Type v} {inst : CommSemiring R} {inst_1 : AddCommMonoid M} {inst_2 : Module R M}
[self : Module.Invertible R M], Function.Bijective ⇑(contractLeft R M)- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Quot.sound
- Assumes
- Module.Invertible
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- TensorProductstatement · cited by 2,545
- Function.Bijectivestatement · cited by 863
- Module.Dualstatement · cited by 583
- Module.Invertiblestatement and proof · cited by 41
- contractLeftstatement · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- Module.Invertible.linearEquivproof · cited by 8
- Module.Invertible.exists_finset_free_localizationproof · cited by 0