Theorems · Theorem · field theory
IntermediateField.cardinalMk_adjoin_le
∀ (F : Type u) [inst : Field F] {E : Type u} [inst_1 : Field E] [inst_2 : Algebra F E] (s : Set E),
Cardinal.mk ↥(IntermediateField.adjoin F s) ≤ max (max (Cardinal.mk F) (Cardinal.mk ↑s)) Cardinal.aleph0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement and proof · cited by 7,166
- Cardinalstatement · cited by 2,598
- IntermediateFieldstatement · cited by 988
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.aleph0statement and proof · cited by 521
- IntermediateField.adjoinstatement and proof · cited by 382
- Cardinal.lift_idproof · cited by 163
- IntermediateField.lift_cardinalMk_adjoin_leproof · cited by 2
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