Theorems · Theorem · group theory
Finset.prod_union_eq_left
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : CommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι],
(∀ a ∈ s₂, a ∉ s₁ → f a = 1) → ∏ a ∈ s₁ ∪ s₂, f a = ∏ a ∈ s₁, f a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 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.
Cites6
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
- CommMonoidstatement and proof · cited by 2,264
- Finset.subset_union_leftproof · cited by 59
- Finset.mem_unionproof · cited by 49
- Finset.prod_subsetproof · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- Finset.prod_union_eq_rightproof · cited by 1