Theorems · Theorem · number theory
NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv
∀ (v : NumberField.InfinitePlace ℚ) (x : WithAbs ↑v), ↑((WithAbs.equiv ↑v) x) = { toCompletion := ↑x }The coercion from the rationals to its completion along an infinite place is Rat.cast.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- RingHomstatement · cited by 10,189
- Complexstatement · cited by 5,565
- RingEquivstatement · cited by 1,147
- RingHom.compproof · cited by 899
- NumberField.InfinitePlacestatement and proof · cited by 604
- RingEquiv.symmproof · cited by 567
- AbsoluteValuestatement · cited by 363
- RingEquiv.toRingHomproof · cited by 150
- UniformSpace.Completion.coe'statement · cited by 144
- WithAbsstatement and proof · cited by 102
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completionproof · cited by 0