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Theorems · Theorem · group theory

Matrix.ProjGenLinGroup.induction_on

∀ {n : Type u_1} {R : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R]
  {motive : Matrix.ProjGenLinGroup n R → Prop} (g : Matrix.ProjGenLinGroup n R),
  (∀ (g : GL n R), motive (Matrix.ProjGenLinGroup.mk g)) → motive g
Defined in
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Projective
Cited by
2 results in Mathlib
Foundations
Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeDecidableEqCommRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.ProjectiveSpecialLinearGroup.toPGL_surj_of_roots · cited by 1ProjectiveSpecialLinearGr…Matrix.ProjGenLinGroup.map_comp · cited by 0ProjGenLinGroup.map_compDFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingFintype · cited by 7736FintypeMatrix · cited by 4303MatrixMonoidHom · cited by 3629MonoidHomMatrix.GeneralLinearGroup · cited by 556Matrix.GeneralLinearGroupMatrix.ProjGenLinGroup · cited by 23Matrix.ProjGenLinGroupMatrix.ProjGenLinGroup.mk · cited by 19ProjGenLinGroup.mkProjGenLinGroup.induction_onCITED BYCITES

Cites8

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Cited by2

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