Theorems · Theorem · group theory
AddSubgroup.addOrderOf_dvd_natCard
∀ {G : Type u_6} [inst : AddGroup G] (s : AddSubgroup G) {x : G}, x ∈ s → addOrderOf x ∣ Nat.card ↥s- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Nat.cardstatement and proof · cited by 844
- addOrderOfstatement · cited by 208
- addOrderOf_dvd_natCardproof · cited by 6
- AddSubgroup.addOrderOf_mkproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.addOrderOf_le_cardproof · cited by 1