constVAdd — Mathlib

English

Repeat: the product of two affine equivalences e1,e2 yields an affine equivalence between product spaces.

Русский

Повтор: произведение двух аффинных эквивалентов даёт аффинное отображение между произведениями пространств.

LaTeX

$$$e_1 \prodCongr e_2 : P_1 \times P_3 \to^a_k P_2 \times P_4$$$

Lean4

/-- The map `p ↦ v +ᵥ p` as an affine automorphism of an affine space.

Note that there is no need for an `AffineMap.constVAdd` as it is always an equivalence.
This is roughly to `DistribMulAction.toLinearEquiv` as `+ᵥ` is to `•`. -/
@[simps! apply linear]
def constVAdd (v : V₁) : P₁ ≃ᵃ[k] P₁ where
  toEquiv := Equiv.constVAdd P₁ v
  linear := LinearEquiv.refl _ _
  map_vadd' _ _ := vadd_comm _ _ _

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