Theorems · Theorem · group theory

Set.powersetCard.coe_smul

∀ {G : Type u_1} [inst : Group G] {α : Type u_2} [inst_1 : MulAction G α] [inst_2 : DecidableEq α] {n : ℕ} {g : G}
  {s : ↑(Set.powersetCard α n)}, ↑(g • s) = g • ↑s

Defined in: Mathlib.GroupTheory.GroupAction.SubMulAction.Combination
Cited by: 2 results in Mathlib
Foundations: Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction DecidableEq

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Cites8

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
MulActionstatement and proof · cited by 1,294
Finset.smulFinsetstatement · cited by 101
Set.powersetCardstatement and proof · cited by 100
SubMulAction.val_smulproof · cited by 2

Cited by2

Results whose statement or proof uses this declaration.

Set.powersetCard.stabilizer_coeproof · cited by 2
Set.powersetCard.mulAction_faithfulproof · cited by 1