English
For HasSubst a, the substitution homomorphism coincides with the evaluation map aeval.
Русский
Для HasSubst a подстановка-подстановка-алгебраическая гомоморфная карта совпадает с отображением aeval.
LaTeX
$$$\\text{ha: HasSubst } a \\implies (MvPowerSeries.substAlgHom ha) = (MvPowerSeries.aeval ha.hasEval).$$$
Lean4
/-- Rewrite `MvPowerSeries.substAlgHom` as `MvPowerSeries.aeval`.
Its use is discouraged because it introduces a topology and might lead
into awkward comparisons. -/
theorem substAlgHom_eq_aeval [UniformSpace R] [DiscreteUniformity R] [UniformSpace S] [DiscreteUniformity S]
(ha : HasSubst a) : (substAlgHom ha : MvPowerSeries σ R → MvPowerSeries τ S) = MvPowerSeries.aeval ha.hasEval :=
by
simp only [substAlgHom, coe_aeval ha.hasEval]
convert coe_aeval (R := R) (hasSubst_iff_hasEval_of_discreteTopology.mp ha) <;> exact DiscreteUniformity.eq_bot.symm
