Theorems · Theorem · number theory
NumberField.InfinitePlace.eq_one_of_rpow_eq
∀ {K : Type u_1} [inst : Field K] {v w : NumberField.InfinitePlace K} {t : ℝ}, (fun x => w x) ^ t = ⇑v → t = 1If v and w are infinite places of K and v = w ^ t for some t then t = 1.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 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.
Cites8
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 and proof · cited by 25,697
- Fieldstatement and proof · cited by 7,404
- NumberField.InfinitePlacestatement and proof · cited by 604
- Real.rpow_oneproof · cited by 114
- NoMaxOrder.exists_gtproof · cited by 62
- NumberField.InfinitePlace.map_natCastproof · cited by 3
- Real.rpow_right_injproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.eq_iff_isEquivproof · cited by 1