instJointlySurjectivePrecoverage — Mathlib

English

The construction gives an instance that for any P, the precoverage P is jointly surjective.

Русский

Построение предоставляет экземпляр, что для любого свойства P предпокрытие P является jointly surjective.

LaTeX

$$$$ \operatorname{instJointlySurjectivePrecoverage}(P) : \operatorname{JointlySurjective}(\operatorname{precoverage} P) $$$$

Lean4

instance : JointlySurjective (precoverage P) where
  exists_eq {X}
    R := fun ⟨hR, _⟩ x ↦
    by
    rw [jointlySurjectivePrecoverage, Presieve.mem_comap_jointlySurjectivePrecoverage_iff] at hR
    obtain ⟨Y, g, hg, heq⟩ := hR x
    use Y, g, hg
    exact heq

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