Theorems · Theorem · geometry

AffineBasis.surjective_coord

∀ {ι : Type u_1} {k : Type u_5} {V : Type u_6} {P : Type u_7} [inst : AddCommGroup V] [inst_1 : AddTorsor V P]
  [inst_2 : Ring k] [inst_3 : Module k V] (b : AffineBasis ι k P) [Nontrivial ι] (i : ι),
  Function.Surjective ⇑(b.coord i)

Defined in: Mathlib.LinearAlgebra.AffineSpace.Basis
Cited by: 1 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommGroup AddTorsor Ring Module Nontrivial

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

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
Finsetproof · cited by 13,712
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Ringstatement and proof · cited by 7,463
Finset.sumproof · cited by 5,195
Nontrivialstatement and proof · cited by 2,416
Finset.sum_congrproof · cited by 2,323
AddTorsorstatement and proof · cited by 1,657
one_smulproof · cited by 1,374
Finset.filterproof · cited by 949
AffineMapstatement · cited by 674

Cited by1

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isOpenMap_barycentric_coordproof · cited by 1