Theorems · Theorem · group theory
Set.powersetCard.fixedPoints_ne_univ_of_faithfulSMul
∀ {G : Type u_1} [inst : Group G] {α : Type u_2} [inst_1 : MulAction G α] [inst_2 : DecidableEq α] [Nontrivial G]
[FaithfulSMul G α] {n : ℕ}, 0 < n → n < Nat.card α → MulAction.fixedPoints G ↑(Set.powersetCard α n) ≠ Set.univ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Set.univstatement and proof · cited by 3,945
- Nontrivialstatement and proof · cited by 2,416
- Equiv.Permproof · cited by 1,375
- MulActionstatement and proof · cited by 1,294
- Nat.cardstatement and proof · cited by 844
- FaithfulSMulstatement and proof · cited by 340
- exists_neproof · cited by 101
- Set.powersetCardstatement and proof · cited by 100
Cited by3
Results whose statement or proof uses this declaration.
- alternatingGroup.normal_subgroup_eq_bot_or_eq_top_of_card_ne_eightproof · cited by 1
- alternatingGroup.normal_subgroup_eq_bot_or_eq_top_of_card_ne_sixproof · cited by 1
- Equiv.Perm.alternatingGroup_le_of_normalproof · cited by 0