Theorems · Theorem · group theory
Finset.prod_subset_one_on_sdiff
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : CommMonoid M] {f g : ι → M} [inst_1 : DecidableEq ι],
s₁ ⊆ s₂ → (∀ x ∈ s₂ \ s₁, g x = 1) → (∀ x ∈ s₁, f x = g x) → ∏ i ∈ s₁, f i = ∏ i ∈ s₂, g i- Cited by
- 4 results in Mathlib
- Foundations
- Depth 66 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.
Cites7
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
- one_mulproof · cited by 2,841
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.prod_congrproof · cited by 646
- Finset.prod_eq_oneproof · cited by 22
- Finset.prod_sdiffproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- Finset.prod_subsetproof · cited by 31
- MeasureTheory.isProjectiveMeasureFamily_piproof · cited by 4
- HasProd.nat_mul_negproof · cited by 2
- Nat.prod_pow_prime_padicValNatproof · cited by 0