Theorems · Theorem · group theory
Subgroup.orderOf_le_card
∀ {G : Type u_6} [inst : Group G] (s : Subgroup G), (↑s).Finite → ∀ {x : G}, x ∈ s → orderOf x ≤ Nat.card ↥s- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Set.Finitestatement and proof · cited by 1,814
- Nat.cardstatement · cited by 844
- orderOfstatement · cited by 324
- Set.Nonempty.to_subtypeproof · cited by 55
- Set.Finite.to_subtypeproof · cited by 44
- Nat.card_pos_iffproof · cited by 6
- OneMemClass.coe_nonemptyproof · cited by 1
- Subgroup.orderOf_dvd_natCardproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Monoid.le_minOrder_iff_forall_subgroupproof · cited by 1