Theorems · Definition · group theory
toAddUnits
{G : Type u_5} → [inst : AddGroup G] → G ≃+ AddUnits GAn additive group is isomorphic to its group of additive units
- Defined in
- Mathlib.Algebra.Group.Units.Equiv
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddEquivstatement · cited by 1,087
- AddUnitsstatement and proof · cited by 325
- neg_add_cancelproof · cited by 256
- AddUnits.valproof · cited by 248
- add_neg_cancelproof · cited by 213
Cited by12
Results whose statement or proof uses this declaration.
- Equiv.addRightproof · cited by 30
- Equiv.addLeftproof · cited by 19
- Set.preimage_vadd_negproof · cited by 10
- val_toAddUnits_applystatement and proof · cited by 4
- HasCompactSupport.convolutionExistsAtproof · cited by 2
- AddSubgroup.mem_ofAddUnits_iff_toAddUnits_memstatement and proof · cited by 1
- toAddUnits_homeomorphproof · cited by 1
- toAddUnits_symm_applystatement and proof · cited by 1
- toAddUnits_val_applystatement and proof · cited by 1
- AddSubgroup.addUnitsEquivSelfproof · cited by 0
- IsTopologicalAddGroup.isOpenMap_iff_nhds_zeroproof · cited by 0
- AddSubgroup.mem_iff_toAddUnits_mem_addUnitsstatement and proof · cited by 0