Theorems · Theorem · field theory
Subfield.map_comap_eq
∀ {K : Type u} {L : Type v} [inst : DivisionRing K] [inst_1 : DivisionRing L] (f : K →+* L) (s : Subfield L),
Subfield.map f (Subfield.comap f s) = s ⊓ f.fieldRange- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingDivisionRing
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.
- RingHomstatement and proof · cited by 10,189
- DivisionRingstatement and proof · cited by 1,062
- SetLike.coe_injectiveproof · cited by 374
- Subfieldstatement and proof · cited by 303
- Set.image_preimage_eq_inter_rangeproof · cited by 121
- RingHom.fieldRangestatement and proof · cited by 40
- Subfield.mapstatement and proof · cited by 30
- Subfield.comapstatement and proof · cited by 29
Cited by3
Results whose statement or proof uses this declaration.
- Subfield.lift_relrank_comapproof · cited by 4
- Subfield.lift_relrank_comap_comap_eq_lift_relrank_infproof · cited by 4
- Subfield.map_comap_eq_selfproof · cited by 0