fst_comp_quotientInfEquivQuotientProd

English

Second projection under the quotient equivalence corresponds to the right quotient factor.

Русский

Вторая компонента эквивален ресурса отвечает за второй фактор факторизации.

LaTeX

$$$\\text{snd}(\\text{quotientInfQuotientProd}) = \\operatorname{Quotient.factor} \\;\\text{inf\_le\_right}$$$

Lean4

@[simp]
theorem fst_comp_quotientInfEquivQuotientProd (I J : Ideal R) (coprime : IsCoprime I J) :
    (RingHom.fst _ _).comp (quotientInfEquivQuotientProd I J coprime : R ⧸ I ⊓ J →+* (R ⧸ I) × R ⧸ J) =
      Ideal.Quotient.factor inf_le_left :=
  by apply Quotient.ringHom_ext; ext; rfl

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