Theorems · Theorem · number theory
NumberField.InfinitePlace.LiesOver.isComplex_of_isComplex_under
∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
(w : NumberField.InfinitePlace L) {v : NumberField.InfinitePlace K} [w.LiesOver v], v.IsComplex → w.IsComplexIf w : InfinitePlace L lies above v : InfinitePlace K and v is complex, then so is w.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Complexproof · cited by 5,565
- Algebra.algebraMapproof · cited by 4,706
- RingHom.compproof · cited by 899
- starRingEndproof · cited by 671
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsComplexstatement and proof · cited by 272
- star_starproof · cited by 135
- NumberField.InfinitePlace.embeddingproof · cited by 78
- NumberField.InfinitePlace.mkproof · cited by 56
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.IsUnramified.finrank_eq_oneproof · cited by 3
- NumberField.InfinitePlace.LiesOver.isReal_of_isReal_overproof · cited by 0