Theorems · Theorem · group theory
Finset.smul_prod_perm
∀ {N : Type u_2} [inst : CommMonoid N] {G : Type u_4} [inst_1 : Group G] [inst_2 : MulDistribMulAction G N]
[inst_3 : Fintype G] (b : N) (g : G), g • ∏ h, h • b = ∏ h, h • b- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Groupstatement and proof · cited by 6,238
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.prod_congrproof · cited by 646
- smul_smulproof · cited by 360
- MulDistribMulActionstatement and proof · cited by 120
- Group.mulLeft_bijectiveproof · cited by 7
- Finset.smul_prod'proof · cited by 3
- Finset.prod_bijectiveproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.IsInvariant.exists_smul_of_under_eqproof · cited by 5
- MulSemiringAction.smul_charpolyproof · cited by 1
- smul_finprod_permproof · cited by 0