Theorems · Theorem · number theory
NumberField.prod_abs_eq_one
∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {x : K},
x ≠ 0 → (∏ w, w x ^ w.mult) * ∏ᶠ (w : NumberField.FinitePlace K), w x = 1The Product Formula for the Number Field K.
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- 0 results in Mathlib
- Foundations
- Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
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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 · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- Finset.univstatement · cited by 3,473
- Finset.prodstatement · cited by 2,356
- absproof · cited by 1,814
- NumberFieldstatement and proof · cited by 653
- NumberField.InfinitePlacestatement · cited by 604
- finprodstatement · cited by 257
- mul_inv_cancel₀proof · cited by 210
- Algebra.normproof · cited by 155
- NumberField.InfinitePlace.multstatement · cited by 107
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