Theorems · Theorem · number theory
NumberField.InfinitePlace.LiesOver.isReal_of_isReal_over
∀ {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], w.IsReal → v.IsRealIf w : InfinitePlace L lies above v : InfinitePlace K and w is real, then so is v.
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- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- NumberField.InfinitePlace.LiesOverstatement and proof · cited by 25
- NumberField.InfinitePlace.not_isComplex_iff_isRealproof · cited by 5
- NumberField.InfinitePlace.LiesOver.isComplex_of_isComplex_underproof · cited by 2
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