hasSubst_iff_hasEval_of_discreteTopology

English

For HasSubst a, having HasEval a is equivalent to HasSubst a in discrete topology settings.

Русский

Для HasSubst a равносильно HasEval a в дискретной топологии.

LaTeX

$$HasSubst a ↔ HasEval a$$

Lean4

/-- A multivariate power series can be substituted if and only if
it can be evaluated when the topology on the coefficients ring is the discrete topology. -/
theorem hasSubst_iff_hasEval_of_discreteTopology [TopologicalSpace S] [DiscreteTopology S] : HasSubst a ↔ HasEval a :=
  by simp_rw [hasSubst_def, hasEval_def, coeff_zero_iff, isTopologicallyNilpotent_iff_constantCoeff_isNilpotent]

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