Theorems · Theorem · number theory
NumberField.mixedEmbedding.normAtAllPlaces_eq_of_normAtComplexPlaces_eq
∀ {K : Type u_1} [inst : Field K] {x y : NumberField.mixedEmbedding.mixedSpace K},
NumberField.mixedEmbedding.normAtComplexPlaces x = NumberField.mixedEmbedding.normAtComplexPlaces y →
NumberField.mixedEmbedding.normAtAllPlaces x = NumberField.mixedEmbedding.normAtAllPlaces y- Cited by
- 1 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- absproof · cited by 1,814
- NumberField.InfinitePlaceproof · cited by 604
- NumberField.InfinitePlace.IsRealproof · cited by 301
- NumberField.InfinitePlace.IsComplexproof · cited by 272
- NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
- NumberField.mixedEmbedding.realSpacestatement · cited by 87
- NumberField.mixedEmbedding.normAtAllPlacesstatement · cited by 30
- NumberField.mixedEmbedding.normAtPlace_apply_of_isComplexproof · cited by 9
- NumberField.InfinitePlace.isReal_or_isComplexproof · cited by 9
- NumberField.mixedEmbedding.normAtPlace_apply_of_isRealproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integralproof · cited by 2