toSpec_injective — Mathlib

English

If I is a prime homogeneous ideal, then it is homogeneous with respect to 𝒜.

Русский

Если I — простый однородный идеал, он однороден по 𝒜.

LaTeX

$$$I \text{ prime} \Rightarrow I\text{ is homogeneous w.r.t. } 𝒜$$$

Lean4

theorem toSpec_injective {f : A} {m : ℕ} (f_deg : f ∈ 𝒜 m) (hm : 0 < m) : Function.Injective (toSpec 𝒜 f) :=
  by
  intro x₁ x₂ h
  have := congr_arg (FromSpec.toFun f_deg hm) h
  rwa [fromSpec_toSpec, fromSpec_toSpec] at this

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