Theorems · Theorem · group theory
IsUnit.smul_bijective
∀ {α : Type u_5} {β : Type u_6} [inst : Monoid α] [inst_1 : MulAction α β] {m : α},
IsUnit m → Function.Bijective fun a => m • a- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- MulActionstatement and proof · cited by 1,294
- Function.Bijectivestatement · cited by 863
- MulAction.bijectiveproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- preimage_smul_setₛₗ_of_isUnit_isUnitproof · cited by 3
- IsLocalization.smul_bijectiveproof · cited by 2