Theorems · Theorem · group theory
Set.powersetCard.addAction_faithful
∀ {α : Type u_2} [inst : DecidableEq α] {G : Type u_3} [inst_1 : AddGroup G] [inst_2 : AddAction G α] {n : ℕ},
1 ≤ n → ↑n < ENat.card α → ∀ {g : G}, AddAction.toPerm g = 1 ↔ AddAction.toPerm g = 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqAddGroupAddAction
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- ENatstatement · cited by 4,985
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddproof · cited by 1,820
- Equiv.Permstatement · cited by 1,375
- AddActionstatement and proof · cited by 820
- Set.powersetCardstatement and proof · cited by 100
- ENat.cardstatement and proof · cited by 89
- AddAction.toPermstatement and proof · cited by 21
- Equiv.Perm.coe_oneproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Set.powersetCard.faithfulVAddproof · cited by 0