w — Mathlib · SciLib

English

The presieve₀ of the sum of two PreZeroHypercovers equals the supremum (max) of their presieve₀'s.

Русский

presieve₀ суммы двух преднулевых гиперобложек равна наивысшей границе их presieve₀.

LaTeX

$$$ (E.sum F).presieve_0 = \\mathrm{SemilatticeSup}.toMax.max \\; E.presieve_0\\ F.presieve_0 $$$

Lean4

theorem w : forkMap P R ≫ firstMap P R = forkMap P R ≫ secondMap P R :=
  by
  dsimp
  ext fg
  simp only [firstMap, secondMap, forkMap]
  simp only [limit.lift_π, limit.lift_π_assoc, assoc, Fan.mk_π_app]
  haveI := Presieve.HasPairwisePullbacks.has_pullbacks fg.1.2.2 fg.2.2.2
  rw [← P.map_comp, ← op_comp, pullback.condition]
  simp

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