Theorems · Theorem · number theory
NumberField.InfinitePlace.card_add_two_mul_card_eq_rank
∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K], NumberField.InfinitePlace.nrRealPlaces K + 2 * NumberField.InfinitePlace.nrComplexPlaces K = Module.finrank ℚ K
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 296 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomproof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexproof · cited by 5,565
- Module.finrankstatement and proof · cited by 1,770
- Fintype.cardproof · cited by 1,386
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlace.nrComplexPlacesstatement and proof · cited by 52
- NumberField.ComplexEmbedding.IsRealproof · cited by 38
- NumberField.InfinitePlace.nrRealPlacesstatement · cited by 33
- Fintype.card_subtype_complproof · cited by 16
- NumberField.Embeddings.cardproof · cited by 6
- Fintype.card_subtype_leproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.nrComplexPlaces_eq_totient_div_twoproof · cited by 4
- NumberField.abs_discr_geproof · cited by 2
- NumberField.IsTotallyComplex.finrankproof · cited by 2
- NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discrproof · cited by 2
- NumberField.InfinitePlace.nrComplexPlaces_eq_zero_of_finrank_eq_oneproof · cited by 2
- NumberField.InfinitePlace.ComplexEmbedding.conjugate_signproof · cited by 1
- NumberField.IsTotallyReal.finrankproof · cited by 1
- NumberField.InfinitePlace.nrRealPlaces_pos_of_odd_finrankproof · cited by 1
- NumberField.InfinitePlace.nrRealPlaces_eq_one_of_finrank_eq_oneproof · cited by 0