Theorems · Theorem · linear algebra
Submodule.eq_top_of_disjoint
∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
[FiniteDimensional K V] (s t : Submodule K V),
Module.finrank K V ≤ Module.finrank K ↥s + Module.finrank K ↥t → Disjoint s t → s ⊔ t = ⊤- Cited by
- 3 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- add_zeroproof · cited by 2,707
- Disjointstatement and proof · cited by 2,201
- le_antisymmproof · cited by 2,068
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- DivisionRingstatement and proof · cited by 1,062
- le_bot_iffproof · cited by 116
- disjoint_iff_inf_leproof · cited by 64
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.sup_span_singleton_eq_top_iffproof · cited by 1
- Submodule.isCompl_iff_disjointproof · cited by 1
- Module.End.iSup_maxGenEigenspace_eq_topproof · cited by 1