Theorems · Theorem · group theory
Finset.prod_ite_mem
∀ {ι : Type u_1} {M : Type u_3} [inst : CommMonoid M] [inst_1 : DecidableEq ι] (s t : Finset ι) (f : ι → M),
(∏ i ∈ s, if i ∈ t then f i else 1) = ∏ i ∈ s ∩ t, f i- Cited by
- 8 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.filter_mem_eq_interproof · cited by 14
- Finset.prod_filterproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepFun_iff_map_fun_eq_pi_mapproof · cited by 6
- ProbabilityTheory.Kernel.indepSets_piiUnionInter_of_disjointproof · cited by 4
- Finset.prod_div_prod_mem_mulSpanproof · cited by 1
- Matrix.coeff_det_one_add_X_smul_eq_sum_minorsproof · cited by 1
- ProbabilityTheory.cond_iInterproof · cited by 1
- MeasureTheory.Measure.pi_pi_finsetproof · cited by 0
- ProbabilityTheory.Kernel.iIndepFun.cond_iInterproof · cited by 0
- Fintype.prod_ite_memproof · cited by 0