Theorems · Theorem · number theory
NumberField.InfinitePlace.card_complex_embeddings
∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
Fintype.card { φ // ¬NumberField.ComplexEmbedding.IsReal φ } = 2 * NumberField.InfinitePlace.nrComplexPlaces K- Cited by
- 2 results in Mathlib
- Foundations
- Depth 176 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.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement and proof · cited by 5,565
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- Finset.cardproof · cited by 2,327
- Finset.sum_congrproof · cited by 2,323
- Fintype.cardstatement and proof · cited by 1,386
- Finset.filterproof · cited by 949
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlaceproof · cited by 604
Cited by2
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