Mathlib Map

Theorems · Definition · number theory

NumberField.InfinitePlace.Completion.equivCompletion

{K : Type u_1} → [inst : Field K] → (v : NumberField.InfinitePlace K) → v.Completion ≃ (↑v).Completion

Completion.toCompletion and Completion.ofCompletion as an equivalence.

Defined in
Mathlib.NumberTheory.NumberField.Completion.InfinitePlace
Cited by
4 results in Mathlib
Foundations
Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Field
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

NumberField.InfinitePlace.Completion.equiv · cited by 2Completion.equivNumberField.InfinitePlace.Completion.isometryEquivCompletion · cited by 1Completion.isometryEquivC…NumberField.InfinitePlace.Completion.ofCompletion_surjective · cited by 1Completion.ofCompletion_s…NumberField.InfinitePlace.Completion.toCompletion_surjective · cited by 0Completion.toCompletion_s…NumberField.InfinitePlace.Completion.equivCompletion_apply · cited by 0Completion.equivCompletio…NumberField.InfinitePlace.Completion.equivCompletion_symm_apply_toCompletion · cited by 0Completion.equivCompletio…Real · cited by 25697RealRingHom · cited by 10189RingHomEquiv · cited by 8337EquivField · cited by 7404FieldComplex · cited by 5565ComplexNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceAbsoluteValue · cited by 363AbsoluteValueNumberField.place · cited by 71NumberField.placeNumberField.InfinitePlace.Completion · cited by 69InfinitePlace.CompletionAbsoluteValue.Completion · cited by 24AbsoluteValue.CompletionNumberField.InfinitePlace.Completion.toCompletion · cited by 20Completion.toCompletionCompletion.equivCompletionCITED BYCITES

Cites11

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

Cited by6

Results whose statement or proof uses this declaration.