Theorems · Theorem · field theory
Subfield.notMem_of_notMem_closure
∀ {K : Type u} [inst : DivisionRing K] {s : Set K} {P : K}, P ∉ Subfield.closure s → P ∉ s- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
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Cites5
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
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement · cited by 303
- Subfield.closurestatement and proof · cited by 39
- Subfield.subset_closureproof · cited by 15
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