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Theorems · Theorem · geometry

Affine.Simplex.independent

∀ {k : Type u_1} {V : Type u_2} {P : Type u_5} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {n : ℕ} (self : Affine.Simplex k P n), AffineIndependent k self.points
Defined in
Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic
Cited by
45 results in Mathlib
Foundations
Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingAddCommGroupModuleAddTorsor

Around this declaration

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

Affine.Simplex.circumsphere_unique_dist_eq · cited by 6Simplex.circumsphere_uniq…Affine.Simplex.affineCombination_mem_affineSpan_faceOpposite_iff · cited by 6Simplex.affineCombination…Affine.Simplex.affineCombination_mem_setInterior_iff · cited by 5Simplex.affineCombination…Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_face · cited by 4ExcenterExists.excenter_n…Affine.Simplex.ExcenterExists.touchpoint_injective · cited by 4ExcenterExists.touchpoint…EuclideanGeometry.exists_circumcenter_eq_of_cospherical_subset · cited by 3EuclideanGeometry.exists_…EuclideanGeometry.exists_circumradius_eq_of_cospherical_subset · cited by 3EuclideanGeometry.exists_…Affine.Triangle.eq_excenter_of_two_zsmul_oangle_eq · cited by 3Triangle.eq_excenter_of_t…Affine.Simplex.sOppSide_affineSpan_faceOpposite_of_pos_of_neg · cited by 3Simplex.sOppSide_affineSp…Affine.Simplex.affineCombination_eq_touchpoint_iff · cited by 3Simplex.affineCombination…Affine.Simplex.touchpointWeights_eq_zero · cited by 3Simplex.touchpointWeights…Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius · cited by 2Triangle.dist_div_sin_oan…EuclideanGeometry.exists_of_range_subset_orthocentricSystem · cited by 2EuclideanGeometry.exists_…Affine.Triangle.dist_orthogonalProjectionSpan_faceOpposite_eq_iff_two_zsmul_oangle_eq · cited by 2Triangle.dist_orthogonalP…Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadius · cited by 2ExcenterExists.affineSpan…Module · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupRing · cited by 7463RingAddTorsor · cited by 1657AddTorsorAffine.Simplex · cited by 471Affine.SimplexAffine.Simplex.points · cited by 391Simplex.pointsAffineIndependent · cited by 144AffineIndependentSimplex.independentCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by45

Results whose statement or proof uses this declaration.