Theorems · Theorem · group theory
AddSubgroup.coe_eq_univ
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, ↑H = Set.univ ↔ H = ⊤- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Top.topstatement · cited by 9,680
- SetLike.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- Set.univstatement · cited by 3,945
- AddSubgroupstatement and proof · cited by 3,232
- SetLike.ext'_iffproof · cited by 78
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.discrete_iff_addCyclicproof · cited by 1
- addCommutator_eq_bot_iff_center_eq_topproof · cited by 1
- AddSubgroup.isComplement'_bot_leftproof · cited by 0
- AddAction.stabilizer_emptyproof · cited by 0
- AddSubgroup.isComplement'_bot_rightproof · cited by 0
- AddAction.stabilizer_finset_emptyproof · cited by 0