Product rule for dimensions: $\dim\big((Y \otimes \mathbb{C}^B) \cap (\mathbb{C}^A \otimes W)\big) = \dim Y \cdot \dim W$

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Product rule for dimensions: $\dim\big((Y \otimes \mathbb{C}^B) \cap (\mathbb{C}^A \otimes W)\big) = \dim Y \cdot \dim W$ · Prove2Me