Theorems · Theorem · group theory
Set.powersetCard.faithfulVAdd
∀ {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 → ∀ [FaithfulVAdd G α], FaithfulVAdd G ↑(Set.powersetCard α n)If an additive group G acts faithfully on α,
then it acts faithfully on powersetCard α n,
provided 1 ≤ n < ENat.card α.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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.Permproof · 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.toPermproof · cited by 21
- FaithfulVAddstatement and proof · cited by 17
- Equiv.Perm.ext_iffproof · cited by 9
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