Theorems · Theorem · group theory
AddSubgroup.IsComplement.card_right
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G} {T : Set G},
AddSubgroup.IsComplement (↑H) T → Nat.card ↑T = H.index- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Nat.cardstatement · cited by 844
- Set.domRestrictproof · cited by 383
- Equiv.transproof · cited by 337
- Nat.card_congrproof · cited by 133
- Quotient.mk''proof · cited by 132
- AddSubgroup.indexstatement · cited by 104
- Equiv.ofBijectiveproof · cited by 70
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.IsComplement.ncard_rightproof · cited by 1