Theorems · Theorem · number theory

NumberField.mixedEmbedding.span_idealLatticeBasis

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  (I : (FractionalIdeal (nonZeroDivisors (NumberField.RingOfIntegers K)) K)ˣ),
  Submodule.span ℤ (Set.range ⇑(NumberField.mixedEmbedding.fractionalIdealLatticeBasis K I)) =
    NumberField.mixedEmbedding.idealLattice K I

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 312 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites25

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Realstatement · cited by 25,697
SetLike.coeproof · cited by 8,199
Fieldstatement and proof · cited by 7,404
Submodulestatement · cited by 7,192
Complexstatement · cited by 5,565
Set.rangestatement · cited by 4,705
Unitsstatement and proof · cited by 2,804
Units.valstatement and proof · cited by 1,966
Submodule.spanstatement · cited by 1,504
Module.Basisstatement · cited by 1,477
nonZeroDivisorsstatement and proof · cited by 895

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalDomain_idealLatticeproof · cited by 1