coeIdeal_differentIdeal — Mathlib

English

The coeIdeal of the different ideal relates to the dual of I via a reciprocal relation.

Русский

coeIdeal различного идеала имеет отношение к двойственной к I через обратное отношение.

LaTeX

$$coeIdeal(differentIdeal) = (dual(A,K,1))^{-1} * something$$

Lean4

theorem coeIdeal_differentIdeal : ↑(differentIdeal A B) = (FractionalIdeal.dual A K (1 : FractionalIdeal B⁰ L))⁻¹ :=
  by
  apply FractionalIdeal.coeToSubmodule_injective
  simp only [FractionalIdeal.coe_div (FractionalIdeal.dual_ne_zero _ _ (@one_ne_zero (FractionalIdeal B⁰ L) _ _ _)),
    FractionalIdeal.coe_coeIdeal, coeSubmodule_differentIdeal A K, inv_eq_one_div, FractionalIdeal.coe_dual_one,
    FractionalIdeal.coe_one]

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