∀ {P : TopCat → Prop} (X Y : CompHausLike P) [inst : CompHausLike.HasProp P (↑X.toTop ⊕ ↑Y.toTop)]
  (s : CategoryTheory.Limits.BinaryCofan X Y),
  CategoryTheory.CategoryStruct.comp (CompHausLike.ofHom P { toFun := Sum.inl, continuous_toFun := ⋯ })
      ((fun s =>
          CompHausLike.ofHom P
            {
              toFun :=
                Sum.elim ⇑(CategoryTheory.ConcreteCategory.hom s.inl) ⇑(CategoryTheory.ConcreteCategory.hom s.inr),
              continuous_toFun := ⋯ })
        s) =
    s.inl