Theorems · Theorem · group theory
AddSubgroup.mem_iff_toAddUnits_mem_addUnits
∀ {G : Type u_2} [inst : AddGroup G] (H : AddSubgroup G) (x : G), toAddUnits x ∈ H.addUnits ↔ x ∈ H- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddEquivstatement · cited by 1,087
- AddUnitsstatement · cited by 325
- AddSubgroup.toAddSubmonoidstatement · cited by 91
- AddSubmonoid.addUnitsstatement · cited by 32
- toAddUnitsstatement and proof · cited by 8
- val_toAddUnits_applyproof · cited by 4
- AddSubgroup.mem_addUnits_iff_val_memproof · cited by 1
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