Theorems · Theorem · field theory
isSeparable_iff_finInsepDegree_eq_one
∀ (F : Type u) [inst : Field F] (K : Type w) [inst_1 : Field K] [inst_2 : Algebra F K], Algebra.IsSeparable F K ↔ Field.finInsepDegree F K = 1
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- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Module.finrankproof · cited by 1,770
- Algebra.IsSeparablestatement · cited by 210
- separableClosureproof · cited by 55
- Field.finInsepDegreestatement and proof · cited by 15
- separableClosure.eq_top_iffproof · cited by 6
- IntermediateField.finrank_eq_one_iff_eq_topproof · cited by 3
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