∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A : C} (P P' : HomotopicalAlgebra.Precylinder A)
  [inst_1 : CategoryTheory.Limits.HasPushout P.i₁ P'.i₀],
  (P.trans P').i₀ = CategoryTheory.CategoryStruct.comp P.i₀ (CategoryTheory.Limits.pushout.inl P.i₁ P'.i₀)