Theorems · Theorem · group theory
MulAction.IsBlock.eq_univ_of_card_lt
∀ {G : Type u_1} [inst : Group G] {X : Type u_2} [inst_1 : MulAction G X] [MulAction.IsPretransitive G X] {B : Set X}
[hX : Finite X], MulAction.IsBlock G B → Nat.card X < B.ncard * 2 → B = Set.univA too large block is equal to univ
- Defined in
- Mathlib.GroupTheory.GroupAction.Blocks
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Groupstatement and proof · cited by 6,238
- Set.univstatement and proof · cited by 3,945
- mul_oneproof · cited by 3,885
- Finitestatement and proof · cited by 3,029
- Set.Nonemptyproof · cited by 2,627
- le_antisymmproof · cited by 2,068
- MulZeroClass.zero_mulproof · cited by 1,625
- MulActionstatement and proof · cited by 1,294
- Nat.cardstatement and proof · cited by 844
- Eq.geproof · cited by 375
- Set.ncardstatement and proof · cited by 344
Cited by3
Results whose statement or proof uses this declaration.
- alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1
- MulAction.IsPreprimitive.of_card_ltproof · cited by 1
- Equiv.Perm.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1