Theorems · Theorem · group theory
AddSubgroup.mem_toAddSubmonoid
∀ {G : Type u_1} [inst : AddGroup G] (K : AddSubgroup G) (x : G), x ∈ K.toAddSubmonoid ↔ x ∈ K- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- AddSubgroupstatement and proof · cited by 3,232
- AddSubmonoidstatement · cited by 1,178
- AddSubgroup.toAddSubmonoidstatement · cited by 91
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.closure_induction_leftproof · cited by 2
- AddSubgroup.mem_addUnits_iff_val_memproof · cited by 1
- AddSubgroup.saturated_iff_zsmulproof · cited by 0
- AddSubgroup.exists_addEquiv_eq_graphproof · cited by 0
- AddSubgroup.gc_toAddSubmonoid_supportproof · cited by 0
- AddSubgroup.exists_eq_graphproof · cited by 0