Theorems · Theorem · number theory
NumberField.InfinitePlace.card_real_embeddings
∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
Fintype.card { φ // NumberField.ComplexEmbedding.IsReal φ } = NumberField.InfinitePlace.nrRealPlaces K- Cited by
- 3 results in Mathlib
- Foundations
- Depth 174 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- Fintype.cardstatement · cited by 1,386
- NumberFieldstatement and proof · cited by 653
- Fintype.card_congrproof · cited by 67
- NumberField.ComplexEmbedding.IsRealstatement · cited by 38
- NumberField.InfinitePlace.nrRealPlacesstatement · cited by 33
- NumberField.InfinitePlace.mkRealproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.card_add_two_mul_card_eq_rankproof · cited by 9
- NumberField.mixedEmbedding.finrankproof · cited by 4
- NumberField.InfinitePlace.ComplexEmbedding.conjugate_signproof · cited by 1