Theorems · Definition · geometry
Projectivization.submodule
{K : Type u_1} →
{V : Type u_2} →
[inst : DivisionRing K] → [inst_1 : AddCommGroup V] → [inst_2 : Module K V] → Projectivization K V → Submodule K VConsider an element of the projectivization as a submodule of V.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Submodulestatement · cited by 7,192
- Submodule.spanproof · cited by 1,504
- DivisionRingstatement and proof · cited by 1,062
- Projectivizationstatement and proof · cited by 111
- Quotient.liftOn'proof · cited by 19
Cited by13
Results whose statement or proof uses this declaration.
- Projectivization.submodule_mkstatement · cited by 3
- Projectivization.submodule_eqstatement and proof · cited by 2
- Projectivization.equivSubmoduleproof · cited by 2
- PSL.iSup_lineStab_eq_topstatement and proof · cited by 1
- PSL.iwasawaTproof · cited by 1
- Projectivization.finrank_submodulestatement · cited by 1
- Projectivization.independent_iff_iSupIndepstatement and proof · cited by 0
- Projectivization.submodule_injectivestatement and proof · cited by 0
- Projectivization.submodule_mk''statement · cited by 0
- Projectivization.mk''_submodulestatement · cited by 0
- Submodule.mem_projectivization_iff_submodule_lestatement and proof · cited by 0
- PSL.iSup_iwasawaT_eq_topproof · cited by 0