Hinduism is, perhaps surprisingly, remarkably compatible with the theorem proven above. if one examines the Hindu creation myths, they describe a Universe that is in fact God. This Universe undergoes a cycle of creation and destruction (called yugas) that take place over a very long time - a cycle that could fit a physical cosmology of a closed Cosmos that explodes in a big bang, expands to some minimum density, and then collapses in a big crunch to explode again. This is a valid cosmological model, and there is some degree of evidence supporting it as scientists ponder the extent of and effect of ``dark matter'' of various sorts and whether or not it suffices to close the Universe gravitationally.
Pure Vedantic Hinduism as described in particular in the Upanishads is monist and either pandeist or panendeist - Brahman is the Universe, we (as Atman or ``God-souls'') are a part of Brahman and Brahman itself, parts separated from the whole to be able to appreciate the whole and ever seeking to rejoin the whole and its perfect state of being as all things. Brahman in the Upanishads is not a being that is worshipped - they make it absolutely clear that Brahman is indifferent to worship and is not the object of worship. Brahman is that in the core of the mind that is pure awareness, a process and not a thing:
That which the mind cannot know, but by which the mind knows, know that alone to be Brahman. Brahman is not that being which is worshipped of men.
That which the eye cannot see, but by which the eye sees, know that alone to be Brahman. Brahman is not that being which is worshipped of men.
That which the ear cannot hear, but by which ear hears, know that alone to be Brahma. Brahman is not the being which is worshipped of men.
If you think you know It well, you indeed know It very little. That whom you see in the beings and gods is but a very little portion of It.Viewing this as a simple riddle, the answer to the riddle is clearly information. The Brahman is all information and all information is self-encoded in the Universe, and is indeed that by which you know at the level of symbolic encoding and macroscopic sensation and yet cannot know as it is information theoretically impossible to encode a high level, compressive, semantic abstraction of the actual state data used to encode it.
The Kena Upanishad
Brahman, therefore, is the raw naked Universe, timeless information. Atman is our finite, information compressive, symbolic, dynamic, entropy rich experience of the Universe, bound to time. Underneath it all Atman is just Brahman - atoms, molecules, elementary particles, energy, all engaged in a zero-entropy dance completely driven by unbreakable natural law, but through a complex alchemy of self-similar self-organized emergent systems, through the powerful but natural process of mutation plus natural selection in a free-energy (information!) rich environment, Atman is the Universe capturing a symbolic model of itself, the mirror through which Brahman, if only for a fleeting time, can see, and experience, itself.
However, Hinduism is also an enormous body of myths and stories and legends in a polytheism, where there isn't just one God, there are many, where humans who are also gods abound, where some of those humans who are gods are self-aware as God and hence able to work miracles and so on. This is all obvious myth, contradicted by experience, etc. If there is a single difference between this ``common'' Hinduism and (say) Christianity, it is that Hinduism at its worst still recognizes that its myths are myths!
No Hindus that I know of (and I have known many, given that I grew up in India) actually think that gods such as Ganesh (the elephant headed God) have objective existence as real beings. They are openly known to be metaphors, anthropomorphic projections of deity onto strange and wonderous teaching stories designed to bring one to a moment of Enlightenment where one realizes that Atman is Brahman, liberating oneself forever from any lesser conception of God. In Hinduism even the Gods require enlightenment, even the Gods are mere Atman striving towards the moment of perfect realization that they are not distinct beings bound to time but rather tiny chips of self-awareness that by their very existence grant the Universe eyes through which It can see itself.
To be fully compatible with the theorem above, Hinduism doesn't have very far to go. Like all ancient religions, it has its more ``orthodox'' sects who take its scriptures far too seriously, it has ties to an ancient and evil caste system, it has unprovable and extremely implausible theistic assertions such as a belief in serial immortality through a process of divine/karmic justice and rebirth, all of it extremely dubious and in many cases socially undesirable expressions of theistic unreason. Hinduism, while generally peaceable, has certainly historically been perfectly capable of divinely sanctioned war, murder, sexual abuse, and portrays plenty of immorality as being moral. Its primary two scriptural epics, the Mahabharata and the Ramayana describe enormous wars filled with love, rape, faith, betrayal, murder, torture, good guys behaving badly and bad guys behaving well, where nearly all of the good guys and the bad guys are Gods, where our wars simply mimic or extend the wars in heaven.
While these are wonderful world literature and among my favorite stories, they are obviously not historically correct and should be treated as the mythologies that they obviously are, not as documents that ultimately obscure the core concept of God as All.
Before leaving Hinduism, it is worth pointing out that there is one rather famous scene in the Mahabharata which illustrates somewhat the paradox of its Vedic orthodoxy when compared to its core Vedantic belief set. The scene is the battlefield above Kurukshetra, where Arjuna, Krishna's best friend who has Krishna as his charioteer, tires of the killing of his cousins. For a moment his determination to act wanes, and he wishes nothing more but to withdraw from all of the horror and violence. To prevent this, to give Arjuna the strength to begin the slaughter that he was predestined to perform to cleanse the earth of evil for a time, Krishna reveals his Visvaroopa, his true self. His true self is all things, all times, all places, all beings. Krishna is Vishnu, Mahavishnu is Brahman, the entirety of being, aware. Arjuna is shown that he is incapable of sin, as it is all a game he is playing with Himself, that he is ever the killer and the killed, the windshield and the bug, the arrow and the heart that is pierced, the suffering and the joyful soul, and throughout it all is Krishna/Brahman, the Universal One that both is all things and fractally experiences all things through all of the eyes that can see.
Take it for what you will.