Theorems · Theorem · field theory
IntermediateField.LinearDisjoint.of_le
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E]
{A B A' B' : IntermediateField F E}, A.LinearDisjoint ↥B → A' ≤ A → B' ≤ B → A'.LinearDisjoint ↥B'If A and B are linearly disjoint, A' and B' are contained in A and B,
respectively, then A' and B' are also linearly disjoint.
- Defined in
- Mathlib.FieldTheory.LinearDisjoint
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
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
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.LinearDisjointstatement and proof · cited by 82
- IntermediateField.LinearDisjoint.of_le_leftproof · cited by 2
- IntermediateField.LinearDisjoint.of_le_rightproof · cited by 1
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