Do Inada Conditions imply Cobb-Douglas Asymptotic Behavior or only a Elasticity of Substitution equal to one

Barelli and De Breu Passoa proved that Inada conditions imply asymptotic Cobb-Douglas behavior of the production function. This was corrected by Litina and Palivos by putting that only the elasticity of substitution is equal to one. We will correct both proof and arguments and come up with a proof without limitations, leaving the conclusion of Barelli unaltered but with a less restrictive proof. Furthermore if Inada conditions apply then the elasticity of substitution is bounded.