Mathlib Map

Theorems · Theorem · number theory

NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] (x : NumberField.mixedEmbedding.realSpace K)
  (w : NumberField.InfinitePlace K), 0 < ↑NumberField.mixedEmbedding.fundamentalCone.expMapBasis x w
Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne
Cited by
7 results in Mathlib
Foundations
Depth 331 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis · cited by 3fundamentalCone.norm_expM…NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image · cited by 2fundamentalCone.setLInteg…NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_image_preimage_expMapBasis · cited by 2fundamentalCone.normAtAll…NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne · cited by 2fundamentalCone.volume_no…NumberField.mixedEmbedding.fundamentalCone.expMapBasis_nonneg · cited by 1fundamentalCone.expMapBas…NumberField.mixedEmbedding.fundamentalCone.nonneg_of_mem_compactSet · cited by 1fundamentalCone.nonneg_of…NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne_eq_image · cited by 1fundamentalCone.normAtAll…Real · cited by 25697RealField · cited by 7404FieldPartialEquiv.source · cited by 964PartialEquiv.sourcePartialHomeomorph.toPartialEquiv · cited by 917PartialHomeomorph.toParti…OpenPartialHomeomorph.toPartialHomeomorph · cited by 851OpenPartialHomeomorph.toP…PartialEquiv.toFun · cited by 821PartialEquiv.toFunOpenPartialHomeomorph.toFun' · cited by 745OpenPartialHomeomorph.toF…NumberField · cited by 653NumberFieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlacePartialEquiv.symm · cited by 453PartialEquiv.symmContinuousLinearEquiv.symm · cited by 368ContinuousLinearEquiv.symmNumberField.mixedEmbedding.realSpace · cited by 87mixedEmbedding.realSpaceHomeomorph.toEquiv · cited by 77Homeomorph.toEquivContinuousLinearEquiv.toHomeomorph · cited by 44ContinuousLinearEquiv.toH…PartialEquiv.restr · cited by 38PartialEquiv.restrfundamentalCone.expMapBasis_p…CITED BYCITES

Cites21

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Cited by7

Results whose statement or proof uses this declaration.