Theorems · Theorem · number theory
NumberField.InfinitePlace.eq_iff_isEquiv
∀ {K : Type u_1} [inst : Field K] {v w : NumberField.InfinitePlace K}, w = v ↔ (↑w).IsEquiv ↑vTwo infinite places v and w are equal if and only if their underlying absolute values
are equivalent.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · 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
- Real.rpow_oneproof · cited by 114
- NumberField.placestatement · cited by 71
- AbsoluteValue.IsEquivstatement and proof · cited by 32
- AbsoluteValue.isEquiv_iff_exists_rpow_eqproof · cited by 4
- NumberField.InfinitePlace.extproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.denseRange_algebraMap_piproof · cited by 1