Theorems · Theorem · group theory
MulAction.bijective
∀ {α : Type u_5} {β : Type u_6} [inst : Group α] [inst_1 : MulAction α β] (g : α), Function.Bijective fun x => g • x- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- Function.Bijectivestatement · cited by 863
- Equiv.bijectiveproof · cited by 132
- MulAction.toPermproof · cited by 30
Cited by11
Results whose statement or proof uses this declaration.
- MulAction.injectiveproof · cited by 24
- MulAction.surjectiveproof · cited by 5
- IsUnit.smul_bijectiveproof · cited by 2
- MulAction.bijective₀proof · cited by 2
- MeasureTheory.Measure.pairwise_aedisjoint_of_aedisjoint_forall_ne_oneproof · cited by 2
- Set.smul_set_piproof · cited by 1
- prodXSubSMul.smulproof · cited by 1
- Set.smul_set_iInterproof · cited by 1
- groupHomology.single_isCycle₁_iffproof · cited by 0
- groupHomology.single_isCycle₂_iffproof · cited by 0
- AddSubgroup.index_smulproof · cited by 0