Theorems · Theorem · group theory
AddSubgroup.card_dvd_of_surjective
∀ {G : Type u_1} {G' : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup G'] (f : G →+ G'),
Function.Surjective ⇑f → Nat.card G' ∣ Nat.card G- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddMonoidHomstatement and proof · cited by 3,230
- Nat.cardstatement and proof · cited by 844
- AddEquiv.toEquivproof · cited by 174
- AddMonoidHom.kerproof · cited by 158
- Nat.card_congrproof · cited by 133
- Dvd.intro_leftproof · cited by 20
- AddSubgroup.card_mul_indexproof · cited by 7
- QuotientAddGroup.quotientKerEquivOfSurjectiveproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- card_dvd_exponent_nsmul_rankproof · cited by 1
- AddSubgroup.card_range_dvdproof · cited by 0
- AddSubgroup.card_map_dvdproof · cited by 0