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1. The Constitution is the supreme law of the land. Any law, customary practice or a decision of an organ of state or a public official which contravenes this Constitution shall be of no effect.
… (Art. 9)

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(2) Citizens may exercise popular participation in the administration of justice through the institutions of public and customary tribunals and the jury and assessor systems.
… (Art. 125)

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b. The Legislature shall enact laws to govern the devolution of estates and establish rights of inheritance and descent for spouses of both statutory and customary marriages so as to give adequate protection to surviving spouses and children of such marriages. (Art. 23)

The State recognizes the traditional leadership [chefferie] as the depositary of customary authority. As such, it participates in the administration of the territory of the Republic in the conditions determined by the law.
The traditional leadership is held to a strict obligation of neutrality and reserve. It is protected against any abuse of power tending to divert it from the role conferred on it by the law. (Art. 167)

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(4) The recognition of the fundamental rights set out in this Chapter¹¹ does not deny the existence of any other rights that are recognized or conferred by Shari'ah, or by customary law or legislation to the extent that they are consistent with the Shari'ah and the Constitution. (Art. 40)

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(4) The state shall work to combat harmful customs and traditions that reduce the dignity and status of women.
… (Art. 48)

1. Except as provided in this Article, no property of any description shall be compulsorily taken possession of, and no interest in or right over property of any description shall be compulsorily acquired, unless by or under the authority of an Act of Parliament which provides for payment of adequate compensation for the property or interest or right to be taken possession of or acquired.
2. Nothing contained in or done under the authority of any law shall be held to be inconsistent with or in contravention of clause (1) to the extent that it is shown that such law provides for the taking possession or acquisition of any property or interest therein or right thereover—
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y. for the purpose of the administration or disposition of such property or interest or right by the President in implementation of a comprehensive land policy or of a policy designed to ensure that the statute law, the Common Law and the doctrines of equity relating to or affecting the interest in or rights over land, or any other interests or right enjoyed by Chiefs and persons claiming through and under them, shall apply with substantial uniformity throughout Zambia;
… (Art. 16)

The freedom of belief, of non-belief, of conscience, of religious opinion, [of] philosophy, of exercise of belief, the freedom of assembly, the free practice of custom as well as the freedom of procession and of demonstration, are guaranteed by this Constitution, under reserve of respect for the law, for public order, for good morals and for the human person. (Art. 7)

(1) The judiciary of Zimbabwe consists of—
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(f) persons presiding over magistrates courts, customary law courts and other courts established by or under an Act of Parliament.
… (Sec. 163)

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The civil and military Courts and Tribunals apply the duly ratified international treaties, the laws, [and] the regulatory acts, provided that they are in conformity with the laws as well as customary [law] unless the latter is contrary to the public order or to morality.
… (Art. 153)