Theorems · Theorem · field theory
IntermediateField.lift_cardinalMk_adjoin_le
∀ (F : Type u) [inst : Field F] {E : Type v} [inst_1 : Field E] [inst_2 : Algebra F E] (s : Set E),
Cardinal.lift.{u, v} (Cardinal.mk ↥(IntermediateField.adjoin F s)) ≤
max (max (Cardinal.lift.{v, u} (Cardinal.mk F)) (Cardinal.lift.{u, v} (Cardinal.mk ↑s))) Cardinal.aleph0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- le_reflproof · cited by 2,061
- IntermediateFieldstatement · cited by 988
- Cardinal.mkstatement and proof · cited by 942
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.rank_sup_leproof · cited by 1
- IntermediateField.cardinalMk_adjoin_leproof · cited by 0