Theorems · Theorem · group theory
PSL.smul_submodule
∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : DecidableEq ι] [inst_2 : Fintype ι]
(g : Matrix.SpecialLinearGroup ι F) (p : Projectivization F (ι → F)), (g • p).submodule = g • p.submodule- Cited by
- 0 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldDecidableEqFintype
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- Matrix.SpecialLinearGroupstatement and proof · cited by 348
- SMulCommClass.smul_commproof · cited by 143
- Projectivizationstatement and proof · cited by 111
- Submodule.pointwiseDistribMulActionstatement · cited by 105
- DistribSMul.toLinearMap_applyproof · cited by 18
- Projectivization.indproof · cited by 15
- Projectivization.submodulestatement · cited by 11
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