Theorems · Theorem · number theory

NumberField.IsCMField.card_infinitePlace_eq_card_infinitePlace

∀ (K : Type u_1) [inst : Field K] [inst_1 : CharZero K] [NumberField.IsCMField K] [inst_3 : NumberField K],
  Fintype.card (NumberField.InfinitePlace ↥(NumberField.maximalRealSubfield K)) =
    Fintype.card (NumberField.InfinitePlace K)

Defined in: Mathlib.NumberTheory.NumberField.CMField
Cited by: 1 results in Mathlib
Foundations: Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field CharZero NumberField.IsCMField NumberField

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Cites22

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
add_zeroproof · cited by 2,707
zero_addproof · cited by 2,366
mul_commproof · cited by 2,262
Module.finrankproof · cited by 1,770
Fintype.cardstatement and proof · cited by 1,386
CharZerostatement and proof · cited by 932
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement and proof · cited by 604
Subfieldstatement · cited by 303
zero_lt_twoproof · cited by 124
NumberField.InfinitePlace.nrComplexPlacesproof · cited by 52

Cited by1

Results whose statement or proof uses this declaration.

NumberField.IsCMField.units_rank_eq_units_rankproof · cited by 2