Theorems · Theorem · group theory
AddAction.injective
∀ {α : Type u_5} {β : Type u_6} [inst : AddGroup α] [inst_1 : AddAction α β] (g : α), Function.Injective fun x => g +ᵥ x- Defined in
- Mathlib.Algebra.Group.Action.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 16 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.
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddstatement · cited by 1,820
- AddActionstatement and proof · cited by 820
- Function.Bijective.injectiveproof · cited by 115
- AddAction.bijectiveproof · cited by 6
Cited by24
Results whose statement or proof uses this declaration.
- Set.vadd_mem_vadd_set_iffproof · cited by 10
- Set.vadd_set_interproof · cited by 10
- Finset.card_vadd_finsetproof · cited by 10
- vadd_left_cancel_iffproof · cited by 7
- Set.vadd_set_sdiffproof · cited by 6
- Finset.vadd_finset_interproof · cited by 4
- Finset.vadd_mem_vadd_finset_iffproof · cited by 3
- Set.disjoint_vadd_setproof · cited by 2
- Cardinal.mk_vadd_setproof · cited by 2
- SubAddAction.ofStabilizer.addConjMap_bijectiveproof · cited by 2
- sbtw_const_vadd_iffproof · cited by 2
- Set.vadd_set_symmDiffproof · cited by 1