isConnected_comma_of_final — Mathlib

English

If A and B are cofiltered and L.Initial, then Comma L R is cofiltered.

Русский

Если A и B кофильтрованы и L.Initial, то Comma L R кофильтрована.

LaTeX

$$$\\\\operatorname{IsCofiltered}(\\\\operatorname{Comma}(L,R))$$$

Lean4

/-- `Comma L R` with `L : A ⥤ T` and `R : B ⥤ T` is connected if `R` is final and `A` is
connected. -/
instance isConnected_comma_of_final [IsConnected A] [R.Final] : IsConnected (Comma L R) := by
  rwa [isConnected_iff_of_final (fst L R)]

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