Theorems · Theorem · number theory
NumberField.IsTotallyReal.finrank
∀ (K : Type u_2) [inst : Field K] [inst_1 : NumberField K] [h : NumberField.IsTotallyReal K], Module.finrank ℚ K = NumberField.InfinitePlace.nrRealPlaces K
- Cited by
- 1 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.
Cites9
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- Module.finrankstatement · cited by 1,770
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlace.nrRealPlacesstatement and proof · cited by 33
- NumberField.IsTotallyRealstatement and proof · cited by 21
- NumberField.InfinitePlace.card_add_two_mul_card_eq_rankproof · cited by 9
- NumberField.nrComplexPlaces_eq_zero_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.card_infinitePlace_eq_card_infinitePlaceproof · cited by 1