Theorems · Theorem · field theory
IntermediateField.LinearDisjoint.finrank_sup
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {A B : IntermediateField F E},
A.LinearDisjoint ↥B → Module.finrank F ↥(A ⊔ B) = Module.finrank F ↥A * Module.finrank F ↥BIf A and B are linearly disjoint over F, then the Module.finrank of
A ⊔ B is equal to the product of that of A and B.
- Defined in
- Mathlib.FieldTheory.LinearDisjoint
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Module.finrankstatement · cited by 1,770
- map_mulproof · cited by 1,137
- IntermediateFieldstatement and proof · cited by 988
- Module.rankproof · cited by 496
- Cardinal.toNatproof · cited by 153
- IntermediateField.LinearDisjointstatement and proof · cited by 82
- IntermediateField.LinearDisjoint.rank_supproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.LinearDisjoint.finrank_left_eq_finrankproof · cited by 2