Complex sentence: This is because it is a tag applied to a "theorem", but qualifying its "proof"; hence, "pure" is here defined in a way which violates the standard proof irrelevance of mathematical theorems.
Split into simpler sentences: This is because it is a tag applied to a "theorem", but qualifying its "proof". They would say that "Pure" is here defined in a way which violates the standard proof irrelevance of mathematical theorems.