Theorems · Theorem · group theory
Finset.prod_const
∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} [inst : CommMonoid M] (b : M), ∏ _x ∈ s, b = b ^ s.card- Cited by
- 154 results in Mathlib
- Foundations
- Depth 22 from the axioms, rests on 191 definitions · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Finset.prodstatement · cited by 2,356
- Finset.cardstatement and proof · cited by 2,327
- CommMonoidstatement and proof · cited by 2,264
- Multiset.prodproof · cited by 528
- Finset.valproof · cited by 438
- Multiset.prod_replicateproof · cited by 40
- Multiset.map_constproof · cited by 9
Cited by154
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepFun.isProbabilityMeasureproof · cited by 14
- Polynomial.resultant_zero_left_degproof · cited by 13
- Matrix.det_smulproof · cited by 11
- Polynomial.resultant_commproof · cited by 11
- NumberField.InfinitePlace.prod_eq_abs_normproof · cited by 8
- AnalyticAt.hasFPowerSeriesAtproof · cited by 7
- Fin.prod_constproof · cited by 6
- IsCoprime.pow_leftproof · cited by 5
- Nat.card_funproof · cited by 5
- Finset.prod_update_of_memproof · cited by 5
- IsCoprime.pow_left_iffproof · cited by 4
- Finset.pow_eq_prod_constproof · cited by 4