Theorems · Theorem · group theory
Subgroup.disjoint_of_coprime_natCard
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G}, (Nat.card ↥H).Coprime (Nat.card ↥K) → Disjoint H K- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 98 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Disjointstatement · cited by 2,201
- Nat.cardstatement and proof · cited by 844
- inf_le_leftproof · cited by 286
- inf_le_rightproof · cited by 238
- disjoint_iffproof · cited by 76
- Nat.eq_one_of_dvd_coprimesproof · cited by 8
- Subgroup.card_dvd_of_leproof · cited by 5
- Subgroup.card_eq_oneproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- IsPGroup.le_or_disjoint_of_coprimeproof · cited by 1
- Subgroup.inf_eq_bot_of_coprimeproof · cited by 0
- Subgroup.isComplement'_of_coprimeproof · cited by 0