Theorems · Theorem · number theory
NumberField.InfinitePlace.prod_eq_prod_mul_prod
∀ {K : Type u_1} [inst : Field K] {α : Type u_2} [inst_1 : CommMonoid α] [inst_2 : NumberField K]
(f : NumberField.InfinitePlace K → α), ∏ w, f w = (∏ w, f ↑w) * ∏ w, f ↑w- Cited by
- 3 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldCommMonoidNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- NumberFieldstatement and proof · cited by 653
- Finset.prod_congrproof · cited by 646
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- NumberField.InfinitePlace.IsComplexstatement and proof · cited by 272
- NumberField.InfinitePlace.not_isReal_iff_isComplexproof · cited by 25
- Equiv.prod_compproof · cited by 20
- Equiv.subtypeEquivRightproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.convexBodyLT_volumeproof · cited by 2
- NumberField.mixedEmbedding.convexBodyLT'_volumeproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_singleproof · cited by 1