of_pullback_snd_of_descendsAlong — Mathlib

English

If P.DescendsAlong Q and HasPullback, then the pullback's second projection satisfies P given Qg and P of pullback.snd.

Русский

Если P descends along Q и есть pullback, то правый компонент пула левой оценки удовлетворяет P при условии Qg и P pullback.snd.

LaTeX

$$$ [P.DescendsAlong Q] [HasPullback f g] (hg : Q g) (hsnd : P (pullback.snd f g)) : P f.$$$

Lean4

theorem of_pullback_snd_of_descendsAlong [P.DescendsAlong Q] [HasPullback f g] (hg : Q g)
    (hsnd : P (pullback.snd f g)) : P f :=
  of_isPullback_of_descendsAlong (IsPullback.of_hasPullback f g).flip hg hsnd

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