Theorems · Theorem · number theory
NumberField.InfinitePlace.mem_orbit_iff
∀ {k : Type u_1} [inst : Field k] {K : Type u_2} [inst_1 : Field K] [inst_2 : Algebra k K] [IsGalois k K]
{w w' : NumberField.InfinitePlace K},
w' ∈ MulAction.orbit Gal(K/k) w ↔ w.comap (algebraMap k K) = w'.comap (algebraMap k K)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexproof · cited by 5,565
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgEquivstatement and proof · cited by 1,681
- RingHom.compproof · cited by 899
- RingHomClass.toRingHomproof · cited by 746
- AlgEquiv.symmproof · cited by 615
- NumberField.InfinitePlacestatement and proof · cited by 604
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.card_isUnramifiedproof · cited by 1
- NumberField.InfinitePlace.card_isUnramified_complproof · cited by 1