Theorems · Theorem · group theory

Set.powersetCard.mulAction_faithful

∀ {G : Type u_1} [inst : Group G] {α : Type u_2} [inst_1 : MulAction G α] {n : ℕ} [inst_2 : DecidableEq α],
  1 ≤ n → ↑n < ENat.card α → ∀ {g : G}, MulAction.toPerm g = 1 ↔ MulAction.toPerm g = 1

Defined in: Mathlib.GroupTheory.GroupAction.SubMulAction.Combination
Cited by: 1 results in Mathlib
Foundations: Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction DecidableEq

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Finsetstatement · cited by 13,712
Set.Elemstatement and proof · cited by 7,166
Groupstatement and proof · cited by 6,238
ENatstatement · cited by 4,985
Equiv.Permstatement · cited by 1,375
MulActionstatement and proof · cited by 1,294
Set.powersetCardstatement and proof · cited by 100
ENat.cardstatement and proof · cited by 89
MulAction.toPermstatement and proof · cited by 30
MulAction.toPerm_applyproof · cited by 12
Equiv.Perm.coe_oneproof · cited by 5

Cited by1

Results whose statement or proof uses this declaration.

Set.powersetCard.faithfulSMulproof · cited by 1