Proof of Theorem 2.7, p. 14 — $i\sim j \iff I_i\mathcal A I_j\neq\{0\}$ is an equivalence relation

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Proof of Theorem 2.7, p. 14 — $i\sim j \iff I_i\mathcal A I_j\neq\{0\}$ is an equivalence relation · Prove2Me