Theorems · Theorem · number theory
NumberField.InfinitePlace.Completion.coe_mul
∀ {K : Type u_1} [inst : Field K] (v : NumberField.InfinitePlace K) (x y : K),
{ toCompletion := ↑(WithAbs.toAbs (↑v) (x * y)) } =
{ toCompletion := ↑(WithAbs.toAbs (↑v) x) } * { toCompletion := ↑(WithAbs.toAbs (↑v) y) }- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- NumberField.InfinitePlacestatement and proof · cited by 604
- AbsoluteValuestatement · cited by 363
- UniformSpace.Completion.coe'statement and proof · cited by 144
- WithAbsstatement · cited by 102
- NumberField.placestatement · cited by 71
- NumberField.InfinitePlace.Completionstatement · cited by 69
- NumberField.InfinitePlace.Completion.extproof · cited by 8
- UniformSpace.Completion.coe_mulproof · cited by 6
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