Theorems · Theorem · group theory
AddAction.IsBlock.ncard_dvd_card
∀ {G : Type u_1} [inst : AddGroup G] {X : Type u_2} [inst_1 : AddAction G X] [AddAction.IsPretransitive G X]
{B : Set X}, AddAction.IsBlock G B → B.Nonempty → B.ncard ∣ Nat.card XThe cardinality of a block divides the cardinality of the ambient type
- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- Set.Nonemptystatement and proof · cited by 2,627
- Nat.cardstatement · cited by 844
- AddActionstatement and proof · cited by 820
- Set.ncardstatement and proof · cited by 344
- AddAction.orbitproof · cited by 86
- AddAction.IsBlockstatement and proof · cited by 65
- AddAction.IsPretransitivestatement and proof · cited by 56
- Dvd.introproof · cited by 26
- AddAction.IsBlock.ncard_block_add_ncard_orbit_eqproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddAction.IsPreprimitive.of_prime_cardproof · cited by 0