Theorems · Theorem · group theory
Finset.prod_subset
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : CommMonoid M] {f : ι → M},
s₁ ⊆ s₂ → (∀ x ∈ s₂, x ∉ s₁ → f x = 1) → ∏ x ∈ s₁, f x = ∏ x ∈ s₂, f x- Cited by
- 31 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.prod_subset_one_on_sdiffproof · cited by 4
Cited by31
Results whose statement or proof uses this declaration.
- Finsupp.prod_of_support_subsetproof · cited by 13
- Finset.prod_eq_single_of_memproof · cited by 5
- Finset.prod_filterproof · cited by 4
- Finset.prod_filter_of_neproof · cited by 3
- Finsupp.prod_mapRange_indexproof · cited by 3
- Finset.prod_eraseproof · cited by 2
- Matrix.BlockTriangular.det_fintypeproof · cited by 2
- centralBinom_factorization_smallproof · cited by 1
- Multipliable.multipliable_of_eq_one_or_selfproof · cited by 1
- Finsupp.multinomial_eq_of_support_subsetproof · cited by 1
- Finset.prod_of_injOnproof · cited by 1
- DFinsupp.prod_add_indexproof · cited by 1