Theorems · Theorem · group theory
smul_left_cancel_iff
∀ {α : Type u_5} {β : Type u_6} [inst : Group α] [inst_1 : MulAction α β] (g : α) {x y : β}, g • x = g • y ↔ x = y- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- MulAction.injectiveproof · cited by 24
Cited by10
Results whose statement or proof uses this declaration.
- IsUnit.smul_left_cancelproof · cited by 9
- MulAction.fixedBy_mem_fixedBy_of_commuteproof · cited by 2
- MulAction.smul_mem_fixedBy_iff_mem_fixedByproof · cited by 2
- HomologicalComplex.mapBifunctorMapHomotopy.comm₁_auxproof · cited by 1
- HomologicalComplex.mapBifunctor₁₂.ι_D₃proof · cited by 1
- HomologicalComplex.mapBifunctorAssociatorX_hom_D₁proof · cited by 1
- MulAction.stabilizer_smul_eq_stabilizer_map_conjproof · cited by 0
- CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Isoproof · cited by 0
- MulAction.Supports.smulproof · cited by 0
- HomologicalComplex.mapBifunctor₂₃.d_eqproof · cited by 0