Theorems · Definition · functional analysis

FormalMultilinearSeries.restrictScalars

(𝕜 : Type u) →
  {𝕜' : Type u'} →
    {E : Type v} →
      {F : Type w} →
        [inst : Semiring 𝕜] →
          [inst_1 : AddCommMonoid E] →
            [inst_2 : Module 𝕜 E] →
              [inst_3 : TopologicalSpace E] →
                [inst_4 : ContinuousAdd E] →
                  [inst_5 : ContinuousConstSMul 𝕜 E] →
                    [inst_6 : AddCommMonoid F] →
                      [inst_7 : Module 𝕜 F] →
                        [inst_8 : TopologicalSpace F] →
                          [inst_9 : ContinuousAdd F] →
                            [inst_10 : ContinuousConstSMul 𝕜 F] →
                              [inst_11 : Semiring 𝕜'] →
                                [inst_12 : SMul 𝕜 𝕜'] →
                                  [inst_13 : Module 𝕜' E] →
                                    [inst_14 : ContinuousConstSMul 𝕜' E] →
                                      [IsScalarTower 𝕜 𝕜' E] →
                                        [inst_16 : Module 𝕜' F] →
                                          [inst_17 : ContinuousConstSMul 𝕜' F] →
                                            [IsScalarTower 𝕜 𝕜' F] →
                                              FormalMultilinearSeries 𝕜' E F → FormalMultilinearSeries 𝕜 E F

Reinterpret a formal 𝕜'-multilinear series as a formal 𝕜-multilinear series.

Defined in

Mathlib.Analysis.Calculus.FormalMultilinearSeries

Cited by

13 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleTopologicalSpaceContinuousAddContinuousConstSMulAddCommMonoidModuleTopologicalSpaceContinuousAddContinuousConstSMulSemiringSMulModuleContinuousConstSMulIsScalarTowerModuleContinuousConstSMulIsScalarTower