Theorems · Definition · linear algebra

LinearEquiv.prodCongr

{R : Type u} →
  {M : Type v} →
    {M₂ : Type w} →
      {M₃ : Type y} →
        {M₄ : Type z} →
          [inst : Semiring R] →
            [inst_1 : AddCommMonoid M] →
              [inst_2 : AddCommMonoid M₂] →
                [inst_3 : AddCommMonoid M₃] →
                  [inst_4 : AddCommMonoid M₄] →
                    {module_M : Module R M} →
                      {module_M₂ : Module R M₂} →
                        {module_M₃ : Module R M₃} →
                          {module_M₄ : Module R M₄} → (M ≃ₗ[R] M₂) → (M₃ ≃ₗ[R] M₄) → (M × M₃) ≃ₗ[R] M₂ × M₄

Product of linear equivalences; the maps come from Equiv.prodCongr.

Defined in

Mathlib.LinearAlgebra.Prod

Cited by

15 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoid