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        "quote": "\n> [!theorem] 双射的复合与逆（随文结论）\n>\n> 若 $\\varphi$ 与 $\\psi$ 都是双射，则<u class=\"concept-term\" data-concept-identity=\"urn:uuid:1ad7f304-3bf4-48cb-a56f-44b509bd7bd7\" data-concept-route=\"/concept-identities#concept-1ad7f304-3bf4-48cb-a56f-44b509bd7bd7\" id=\"first-30aee277558d95155bf2-zh\">复合(composition)</u>也是双射，而且\n>\n> $$\n> (\\psi\\circ\\varphi)^{-1}=\\varphi^{-1}\\circ\\psi^{-1}.\n> $$\n\n> [!proof]- 证明\n>\n> 利用结合律与恒等映射，\n>\n> $$\n> \\varphi^{-1}\\circ\\psi^{-1}\\circ\\psi\\circ\\varphi\n> =\\varphi^{-1}\\circ\\operatorname{id}_Y\\circ\\varphi\n> =\\operatorname{id}_X.\n> $$\n>\n> 反方向的复合也得到相应陪域的恒等映射。\n",
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