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While I would be glad to hear a nicer proof of the Theorem,

Sorry for late answer. You can get a rather quick proof of this theorem by remarking that, in you your situation, when H is cocommutative, the comultiplication is a morphism of bi-algebras.

2 added 7 characters in body

While I would be glad to hear a nicer proof of the Theorem,

Sorry for late answer. You can get a rather quick proof of this theorem by remarking that, in you situation, when H is cocommutative, the comultiplication is a morphism of algebrasbi-algebras.

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While I would be glad to hear a nicer proof of the Theorem,

Sorry for late answer. You can get a rather quick proof of this theorem by remarking that, in you situation, when H is cocommutative, the comultiplication is a morphism of algebras.