range_glueDataObjι — Mathlib

English

The same equality as before but stated with the range of the composed map and the intersection form.

Русский

Та же равенство, но записанная через диапазон композиции и форму пересечения.

LaTeX

$$$ \\text{range }(I.glueDataObjι U ≫ U.1.ι).base = (I.support : Set X) \\cap U $$$

Lean4

theorem range_glueDataObjι (U : X.affineOpens) :
    Set.range (I.glueDataObjι U).base = U.2.isoSpec.inv.base '' PrimeSpectrum.zeroLocus (I.ideal U) :=
  by
  simp only [glueDataObjι, Scheme.comp_coeBase, TopCat.coe_comp, Set.range_comp]
  erw [range_comap_of_surjective]
  swap; · exact Ideal.Quotient.mk_surjective
  simp only [Ideal.mk_ker, CommRingCat.hom_ofHom]

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