Theorems · Definition · linear algebra

Module.subsingletonEquiv

(R : Type u_4) →
  (M : Type u_5) →
    (ι : Type u_6) →
      [inst : Semiring R] → [Subsingleton R] → [inst_2 : AddCommMonoid M] → [inst_3 : Module R M] → M ≃ₗ[R] ι →₀ R

If Subsingleton R, then M ≃ₗ[R] ι →₀ R for any type ι.

Defined in: Mathlib.LinearAlgebra.Finsupp.Defs
Cited by: 4 results in Mathlib
Foundations: Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring Subsingleton AddCommMonoid Module

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

Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
Finsuppstatement and proof · cited by 5,255
LinearEquivstatement · cited by 3,317

Cited by5

Results whose statement or proof uses this declaration.

Module.Basis.reindexRangeproof · cited by 16
Module.Basis.reindexRange_selfproof · cited by 4
Module.subsingletonEquiv.congr_simpstatement and proof · cited by 0
Module.subsingletonEquiv_applystatement and proof · cited by 0
Module.subsingletonEquiv_symm_applystatement and proof · cited by 0