Theorems · Theorem · group theory
Subgroup.coe_eq_singleton
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, (∃ g, ↑H = {g}) ↔ H = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- Group
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
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Bot.botstatement and proof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- SetLike.ext'_iffproof · cited by 78
- Subgroup.eq_bot_of_subsingletonproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.isComplement'_top_leftproof · cited by 1
- Subgroup.isComplement'_top_rightproof · cited by 0