Theorems · Theorem · field theory
IntermediateField.extendScalars_adjoin
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {K : IntermediateField F E}
{S : Set E} (h : K ≤ IntermediateField.adjoin F S),
IntermediateField.extendScalars h = IntermediateField.adjoin (↥K) S- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
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
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- le_antisymmproof · cited by 2,068
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- Set.subset_union_rightproof · cited by 123
- Set.union_subsetproof · cited by 71
- IntermediateField.restrictScalarsproof · cited by 66
- IntermediateField.subset_adjoinproof · cited by 59
- IntermediateField.adjoin_le_iffproof · cited by 28
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