Theorems · Theorem · field theory
Subfield.relfinrank_eq_finrank_of_le
∀ {E : Type v} [inst : Field E] {A B : Subfield E} (h : A ≤ B),
A.relfinrank B = Module.finrank ↥A ↥(Subfield.extendScalars h)If A ≤ B, then Subfield.relfinrank A B is [B : A].
- Defined in
- Mathlib.FieldTheory.Relrank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Module.finrankstatement · cited by 1,770
- IntermediateFieldstatement · cited by 988
- Subfieldstatement and proof · cited by 303
- Cardinal.toNatproof · cited by 153
- Subfield.relfinrankstatement · cited by 23
- Subfield.extendScalarsstatement · cited by 17
- Subfield.relrank_eq_rank_of_leproof · cited by 7
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