Theorems · Theorem · number theory

RingOfIntegers.algebraMap_norm_algebraMap

∀ {L : Type u_1} (K : Type u_2) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
  (x : NumberField.RingOfIntegers K),
  (algebraMap (NumberField.RingOfIntegers K) K)
      ((RingOfIntegers.norm K) ((algebraMap (NumberField.RingOfIntegers K) (NumberField.RingOfIntegers L)) x)) =
    (Algebra.norm K) ((algebraMap K L) ((algebraMap (NumberField.RingOfIntegers K) K) x))

Defined in: Mathlib.NumberTheory.NumberField.Norm
Cited by: 1 results in Mathlib
Foundations: Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra

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Cites9

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

DFunLike.coestatement · cited by 62,936
Algebrastatement and proof · cited by 11,388
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Algebra.algebraMapstatement · cited by 4,706
MonoidHomstatement · cited by 3,629
NumberField.RingOfIntegersstatement and proof · cited by 413
Algebra.normstatement · cited by 155
RingOfIntegers.normstatement · cited by 9

Cited by1

Results whose statement or proof uses this declaration.

RingOfIntegers.norm_algebraMapproof · cited by 1