∀ {α₁ : Type u_9} {β₁ : Type u_11} {β₂ : Type u_12} (e : α₁ → β₁ ≃ β₂),
  (Equiv.sigmaCongrRight e).trans (Equiv.sigmaEquivProd α₁ β₂) =
    (Equiv.sigmaEquivProd α₁ β₁).trans (Equiv.prodCongrRight e)