Theorems · Theorem · group theory
prod_apply
∀ {F : Type u_8} {α : Type u_9} {β : Type u_10} {ι : Type u_11} [inst : FunLike F α β] [inst_1 : CommMonoid β]
[inst_2 : CommMonoid F] [IsOneApply F α β] [IsMulApply F α β] (s : Finset ι) (f : ι → F) (x : α),
(∏ i ∈ s, f i) x = ∏ i ∈ s, (f i) x- Defined in
- Mathlib.Algebra.BigOperators.Pi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 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.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- FunLikestatement and proof · cited by 2,560
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.induction_onproof · cited by 167
- Finset.prod_insertproof · cited by 109
- IsMulApplystatement and proof · cited by 18
- IsOneApplystatement and proof · cited by 12
- one_applyproof · cited by 3
- mul_applyproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- FunLike.coe_prodproof · cited by 0