∀ {J : CategoryTheory.Limits.MulticospanShape} {C : Type u_1} [inst : CategoryTheory.Category.{u_4, u_1} C]
  {F G : CategoryTheory.Functor (CategoryTheory.Limits.WalkingMulticospan J) C},
  (∀ (i : J.L),
      F.obj (CategoryTheory.Limits.WalkingMulticospan.left i) =
        G.obj (CategoryTheory.Limits.WalkingMulticospan.left i)) →
    ∀ (i : J.R),
      F.obj (CategoryTheory.Limits.WalkingMulticospan.left (J.fst i)) =
        G.obj (CategoryTheory.Limits.WalkingMulticospan.left (J.fst i))