Theorems · Theorem · group theory
Finset.prod_update_of_mem
∀ {ι : Type u_1} {M : Type u_3} [inst : CommMonoid M] [inst_1 : DecidableEq ι] {s : Finset ι} {i : ι},
i ∈ s → ∀ (f : ι → M) (b : M), ∏ x ∈ s, Function.update f i b x = b * ∏ x ∈ s \ {i}, f x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 82 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.
Cites11
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
- pow_oneproof · cited by 894
- Finset.prod_congrproof · cited by 646
- Function.updatestatement · cited by 502
- Finset.prod_constproof · cited by 154
- Finset.card_singletonproof · cited by 144
- Finset.inter_singleton_of_memproof · cited by 8
- Finset.prod_piecewiseproof · cited by 2
- Finset.update_eq_piecewiseproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- MultilinearMap.norm_image_sub_le_of_boundproof · cited by 3
- Fintype.card_filter_piFinset_eq_of_memproof · cited by 2
- Module.Basis.det_adjustToOrientationproof · cited by 2
- Module.Basis.orientation_neg_singleproof · cited by 1
- Matrix.adjugate_diagonalproof · cited by 1