Theorems · Definition · field theory
Subfield.copy
{K : Type u} → [inst : DivisionRing K] → (S : Subfield K) → (s : Set K) → s = ↑S → Subfield KCopy of a subfield with a new carrier equal to the old one. Useful to fix definitional
equalities.
- Defined in
- Mathlib.Algebra.Field.Subfield.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 51 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- DivisionRingstatement and proof · cited by 1,062
- Subringproof · cited by 602
- Subfieldstatement and proof · cited by 303
- Subfield.toSubringproof · cited by 23
- Subring.copyproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- RingHom.fieldRangeproof · cited by 40
- FixedPoints.subfieldproof · cited by 20
- Subfield.copy_eqstatement and proof · cited by 0
- Subfield.coe_copystatement · cited by 0