Theorems · Theorem · group theory
AddSubgroup.card_eq_one
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, Nat.card ↥H = 1 ↔ H = ⊥- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- 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.
- Bot.botstatement · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Nat.cardstatement · cited by 844
- le_bot_iffproof · cited by 116
- AddSubgroup.relIndex_bot_leftproof · cited by 4
- AddSubgroup.relIndex_eq_oneproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.disjoint_of_coprime_natCardproof · cited by 1