comp_subst — Mathlib

English

If HasSubst a holds and all spaces carry discrete uniformities, then the substitution map is continuous.

Русский

Если имеет HasSubst a и пространства имеют дискретную униформность, подстановка непрерывна.

LaTeX

$$$\\text{ha: HasSubst } a \\Rightarrow [\\text{UniformSpace } R] [\\text{DiscreteUniformity } R] [\\text{UniformSpace } S] [\\text{DiscreteUniformity } S] \\Rightarrow \\text{Continuous}(\\operatorname{subst} a)$$$

Lean4

theorem comp_subst [UniformSpace R] [DiscreteUniformity R] [UniformSpace S] [DiscreteUniformity S] (ha : HasSubst a)
    (hε : Continuous ε) : ε ∘ (subst a) = aeval (R := R) (ha.hasEval.map hε) := by
  rw [← comp_substAlgHom ha hε, AlgHom.coe_comp, coe_substAlgHom]

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