Tensor products of subspaces intersect factorwise: $(A \otimes B) \cap (A' \otimes B') = (A \cap A') \otimes (B \cap B')$

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Tensor products of subspaces intersect factorwise: $(A \otimes B) \cap (A' \otimes B') = (A \cap A') \otimes (B \cap B')$ · Prove2Me