Theorems · Theorem · linear algebra
Submodule.sup_span_singleton_eq_top_iff
∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [Module.Finite K V]
{W : Submodule K V} {v : V}, v ∉ W → (W ⊔ K ∙ v = ⊤ ↔ Module.finrank K (V ⧸ W) = 1)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Bot.botproof · cited by 4,720
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Module.finrankstatement and proof · cited by 1,770
- add_commproof · cited by 1,535
- Submodule.spanstatement and proof · cited by 1,504
- eq_or_neproof · cited by 1,117
- DivisionRingstatement and proof · cited by 1,062
Cited by1
Results whose statement or proof uses this declaration.