Theorems · Theorem · number theory
NumberField.IsTotallyComplex.finrank
∀ (K : Type u_2) [inst : Field K] [inst_1 : NumberField K] [h : NumberField.IsTotallyComplex K], Module.finrank ℚ K = 2 * NumberField.InfinitePlace.nrComplexPlaces K
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- zero_addproof · cited by 2,366
- Module.finrankstatement · cited by 1,770
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlace.nrComplexPlacesstatement and proof · cited by 52
- NumberField.IsTotallyComplexstatement and proof · cited by 19
- NumberField.InfinitePlace.card_add_two_mul_card_eq_rankproof · cited by 9
- NumberField.nrRealPlaces_eq_zero_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.card_infinitePlace_eq_card_infinitePlaceproof · cited by 1
- NumberField.abs_discr_ge_of_isTotallyComplexproof · cited by 1