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Theorems · Theorem · linear algebra

Module.Basis.singleton_apply

∀ (ι : Type u_7) (R : Type u_8) [inst : Unique ι] [inst_1 : Semiring R] (i : ι), (Module.Basis.singleton ι R) i = 1
Defined in
Mathlib.LinearAlgebra.Basis.Basic
Cited by
4 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniqueSemiring
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Around this declaration

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

OrthonormalBasis.singleton_apply · cited by 3OrthonormalBasis.singleto…Module.Basis.coe_singleton · cited by 3Basis.coe_singletonRat.numberField_discr · cited by 2Rat.numberField_discrLinearMap.toMatrix_singleton · cited by 1LinearMap.toMatrix_single…DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringModule.Basis · cited by 1477Module.BasisUnique · cited by 400UniqueModule.Basis.singleton · cited by 15Basis.singletonModule.Basis.apply_eq_iff · cited by 12Basis.apply_eq_iffBasis.singleton_applyCITED BYCITES

Cites6

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Cited by4

Results whose statement or proof uses this declaration.