Theorems · Theorem · number theory
NumberField.InfinitePlace.nrRealPlaces_eq_one_of_finrank_eq_one
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K],
Module.finrank ℚ K = 1 → NumberField.InfinitePlace.nrRealPlaces K = 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
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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 and proof · cited by 1,770
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlace.nrComplexPlacesproof · cited by 52
- NumberField.InfinitePlace.nrRealPlacesstatement and proof · cited by 33
- NumberField.InfinitePlace.card_add_two_mul_card_eq_rankproof · cited by 9
- NumberField.InfinitePlace.nrComplexPlaces_eq_zero_of_finrank_eq_oneproof · cited by 2
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