congrRight — Mathlib

English

A bijection e : γ ≃ α induces a uniform isomorphism between γ →ᵤ β and α →ᵤ β by precomposition, yielding a UniformEquiv.

Русский

Билинейное отображение e : γ ≃ α порождает равномерное изоморфизм между γ →ᵤ β и α →ᵤ β через предсоставление, образуя UniformEquiv.

LaTeX

$$$$ \text{congrLeft}(e): (γ \to^{u} β) \simeq_{u} (α \to^{u} β) $$$$

Lean4

/-- Turn a uniform isomorphism `γ ≃ᵤ β` into a uniform isomorphism `(α →ᵤ γ) ≃ᵤ (α →ᵤ β)` by
post-composing. -/
protected def congrRight [UniformSpace γ] (e : γ ≃ᵤ β) : (α →ᵤ γ) ≃ᵤ (α →ᵤ β) :=
  {
    Equiv.piCongrRight fun _ =>
      e.toEquiv with
    uniformContinuous_toFun := UniformFun.postcomp_uniformContinuous e.uniformContinuous
    uniformContinuous_invFun := UniformFun.postcomp_uniformContinuous e.symm.uniformContinuous }

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