Theorems · Theorem · field theory
IntermediateField.rank_sup_le
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (A B : IntermediateField F E),
Module.rank F ↥(A ⊔ B) ≤ Module.rank F ↥A * Module.rank F ↥B- Cited by
- 1 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- SetLike.coeproof · cited by 8,199
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- Algebra.algebraMapproof · cited by 4,706
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- le_reflproof · cited by 2,061
- IntermediateFieldstatement and proof · cited by 988
- Cardinal.mkproof · cited by 942
- Cardinal.liftproof · cited by 583
- Cardinal.aleph0proof · cited by 521
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.LinearDisjoint.rank_supproof · cited by 1