Mathlib Map

Theorems · Definition · number theory

NumberField.InfinitePlace.nrRealPlaces

(K : Type u_1) → [inst : Field K] → [NumberField K] → ℕ

The number of infinite real places of the number field K.

Defined in
Mathlib.NumberTheory.NumberField.InfinitePlace.Basic
Cited by
33 results in Mathlib
Foundations
Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.mixedEmbedding.convexBodyLTFactor · cited by 13mixedEmbedding.convexBody…NumberField.InfinitePlace.card_add_two_mul_card_eq_rank · cited by 9InfinitePlace.card_add_tw…NumberField.mixedEmbedding.convexBodyLT'Factor · cited by 6mixedEmbedding.convexBody…NumberField.mixedEmbedding.finrank · cited by 4mixedEmbedding.finrankIsCyclotomicExtension.Rat.nrComplexPlaces_eq_totient_div_two · cited by 4Rat.nrComplexPlaces_eq_to…NumberField.dedekindZeta_residue · cited by 4NumberField.dedekindZeta_…NumberField.mixedEmbedding.convexBodySumFactor · cited by 4mixedEmbedding.convexBody…NumberField.InfinitePlace.card_real_embeddings · cited by 3InfinitePlace.card_real_e…IsCyclotomicExtension.Rat.nrRealPlaces_eq_zero · cited by 3Rat.nrRealPlaces_eq_zeroNumberField.nrRealPlaces_eq_zero_iff · cited by 3NumberField.nrRealPlaces_…NumberField.Ideal.tendsto_norm_le_div_atTop₀ · cited by 2Ideal.tendsto_norm_le_div…NumberField.InfinitePlace.nrComplexPlaces_eq_zero_of_finrank_eq_one · cited by 2InfinitePlace.nrComplexPl…NumberField.InfinitePlace.card_eq_nrRealPlaces_add_nrComplexPlaces · cited by 2InfinitePlace.card_eq_nrR…NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral · cited by 2mixedEmbedding.volume_eq_…NumberField.abs_discr_ge · cited by 2NumberField.abs_discr_geField · cited by 7404FieldFintype.card · cited by 1386Fintype.cardNumberField · cited by 653NumberFieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.IsReal · cited by 301InfinitePlace.IsRealInfinitePlace.nrRealPlacesCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by37

Results whose statement or proof uses this declaration.