Theorems · Theorem · group theory
Finset.card_smul_finset
∀ {α : Type u_2} {β : Type u_3} [inst : DecidableEq β] [inst_1 : Group α] [inst_2 : MulAction α β] (a : α)
(s : Finset β), (a • s).card = s.card- Cited by
- 12 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqGroupMulAction
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Groupstatement and proof · cited by 6,238
- Finset.cardstatement · cited by 2,327
- MulActionstatement and proof · cited by 1,294
- Finset.smulFinsetstatement · cited by 101
- Finset.card_image_of_injectiveproof · cited by 41
- MulAction.injectiveproof · cited by 24
Cited by12
Results whose statement or proof uses this declaration.
- MulAction.mem_stabilizer_finset_iff_subset_smul_finsetproof · cited by 2
- Finset.mulETransformLeft.cardproof · cited by 1
- Finset.pow_ssubset_pow_succ_of_pow_ne_closureproof · cited by 1
- Finset.mulETransformRight.cardproof · cited by 1
- Finset.card_inv_mul_of_doubling_lt_three_halvesproof · cited by 1
- MulAction.mem_stabilizer_finset_iff_smul_finset_subsetproof · cited by 1
- cauchy_davenport_minOrder_mulproof · cited by 1
- Finset.op_smul_convolution_eq_convolution_smulproof · cited by 0
- Finset.dens_smul_finsetproof · cited by 0
- Finset.mulDysonETransform.cardproof · cited by 0
- Finset.univ_convolutionproof · cited by 0
- alternatingGroup.map_kleinFour_conjproof · cited by 0