Theorems · Definition · geometry

AffineEquiv.congrLeft

{k : Type u_1} →
  {P₁ : Type u_2} →
    {P₂ : Type u_3} →
      {V₁ : Type u_6} →
        {V₂ : Type u_7} →
          [inst : Ring k] →
            [inst_1 : AddCommGroup V₁] →
              [inst_2 : AddCommGroup V₂] →
                [inst_3 : Module k V₁] →
                  [inst_4 : Module k V₂] →
                    [inst_5 : AddTorsor V₁ P₁] →
                      [inst_6 : AddTorsor V₂ P₂] →
                        (R : Type u_10) →
                          {W : Type u_11} →
                            [inst_7 : Ring R] →
                              [inst_8 : AddCommGroup W] →
                                [inst_9 : Module k W] →
                                  [inst_10 : Module R W] →
                                    [inst_11 : SMulCommClass k R W] →
                                      (P₁ ≃ᵃ[k] P₂) →
                                        (Q : Type u_12) → [inst_12 : AddTorsor W Q] → (P₁ →ᵃ[k] Q) ≃ᵃ[R] P₂ →ᵃ[k] Q

An affine isomorphism between the domains of affine spaces induces an affine isomorphism over another ring between the two function spaces.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineEquiv

Cited by

2 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModuleAddTorsorAddTorsorRingAddCommGroupModuleModuleSMulCommClassAddTorsor