Theorems · Theorem · field theory
Subfield.div_mem
∀ {K : Type u} [inst : DivisionRing K] (s : Subfield K) {x y : K}, x ∈ s → y ∈ s → x / y ∈ sA subfield is closed under division.
- Defined in
- Mathlib.Algebra.Field.Subfield.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
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- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement and proof · cited by 303
- div_memproof · cited by 9
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