Theorems · Theorem · linear algebra

Module.Basis.coe_ofVectorSpace

∀ (K : Type u_3) (V : Type u_4) [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V],
  ⇑(Module.Basis.ofVectorSpace K V) = Subtype.val

Defined in: Mathlib.LinearAlgebra.Basis.VectorSpace
Cited by: 4 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DivisionRing AddCommGroup Module

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

Cites10

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

DFunLike.coestatement · cited by 62,936
Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Set.Elemstatement and proof · cited by 7,166
Module.Basisstatement · cited by 1,477
DivisionRingstatement and proof · cited by 1,062
Module.Basis.ofVectorSpacestatement · cited by 30
Module.Basis.ofVectorSpaceIndexstatement and proof · cited by 29
Module.Basis.ofVectorSpace_apply_selfproof · cited by 3

Cited by4

Results whose statement or proof uses this declaration.

Submodule.eq_top_of_finrank_eqproof · cited by 15
LinearMap.exists_leftInverse_of_injectiveproof · cited by 6
coevaluation_apply_oneproof · cited by 3
exists_subset_affineIndependent_affineSpan_eq_topproof · cited by 1