Theorems · Theorem · number theory

NumberField.IsCMField.equivInfinitePlace_symm_apply

∀ (K : Type u_1) [inst : Field K] [inst_1 : CharZero K] [inst_2 : NumberField.IsCMField K] [inst_3 : NumberField K]
  (w : NumberField.InfinitePlace ↥(NumberField.maximalRealSubfield K)) (x : ↥(NumberField.maximalRealSubfield K)),
  ((NumberField.IsCMField.equivInfinitePlace K).symm w) ((algebraMap (↥(NumberField.maximalRealSubfield K)) K) x) = w x

Defined in: Mathlib.NumberTheory.NumberField.CMField
Cited by: 1 results in Mathlib
Foundations: Depth 304 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field CharZero NumberField.IsCMField NumberField

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Cites17

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 and proof · cited by 25,697
RingHomstatement · cited by 10,189
Equivstatement · cited by 8,337
Fieldstatement and proof · cited by 7,404
Algebra.algebraMapstatement and proof · cited by 4,706
Equiv.symmstatement and proof · cited by 3,681
CharZerostatement and proof · cited by 932
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement and proof · cited by 604
Equiv.apply_symm_applyproof · cited by 346
Subfieldstatement · cited by 303

Cited by1

Results whose statement or proof uses this declaration.

NumberField.IsCMField.regOfFamily_realFunSystemproof · cited by 1