Theorems · Theorem · field theory
IntermediateField.LinearDisjoint.iff_inf_eq_bot
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {A B : IntermediateField F E}
[IsGalois F ↥A] [FiniteDimensional F ↥A] [FiniteDimensional F ↥B], A.LinearDisjoint ↥B ↔ A ⊓ B = ⊥- Defined in
- Mathlib.FieldTheory.LinearDisjoint
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- 0 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- Bot.botstatement and proof · cited by 4,720
- FiniteDimensionalstatement and proof · cited by 1,854
- IntermediateFieldstatement and proof · cited by 988
- IsGaloisstatement and proof · cited by 149
- IntermediateField.LinearDisjointstatement and proof · cited by 82
- IntermediateField.LinearDisjoint.inf_eq_botproof · cited by 2
- IntermediateField.LinearDisjoint.of_inf_eq_botproof · cited by 2
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