Theorems · Definition · field theory
Subfield.subtype
{K : Type u} → [inst : DivisionRing K] → (s : Subfield K) → ↥s →+* KThe embedding from a subfield of the field K to K.
- Defined in
- Mathlib.Algebra.Field.Subfield.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- MonoidHomproof · cited by 3,629
- AddMonoidHomproof · cited by 3,230
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement and proof · cited by 303
- Subsemiring.toSubmonoidproof · cited by 153
- AddSubgroup.subtypeproof · cited by 82
- Subring.toSubsemiringproof · cited by 71
- Submonoid.subtypeproof · cited by 26
- Subfield.toSubringproof · cited by 23
- Subfield.toAddSubgroupproof · cited by 2
Cited by17
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.mk_eq_iffproof · cited by 5
- Subfield.inclusionproof · cited by 4
- NumberField.IsTotallyReal.le_maximalRealSubfieldproof · cited by 3
- Matrix.mem_subfield_of_mul_eq_one_of_mem_subfield_rightproof · cited by 1
- Subfield.toSubring_subtype_eq_subtypestatement · cited by 1
- Complex.uniformContinuous_ringHom_eq_id_or_conjstatement and proof · cited by 1
- Subfield.algebraMap_ofSubfieldstatement · cited by 1
- FixedPoints.minpoly.of_eval₂statement and proof · cited by 1
- Subfield.fieldRange_subtypestatement and proof · cited by 1
- max_aleph0_card_le_rank_fun_natproof · cited by 1
- Subfield.subtype_applystatement · cited by 0
- Subfield.subtype_injectivestatement · cited by 0