"law of double negation" meaning in English

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      "examples": [
        {
          "text": "The law of double negation is not valid intuitionistically. To show this with Heyting algebra semantics, let A=(0,1)∪(1,2). Then ¬A=(-∞,0)∪(2,∞), ¬¬A=(0,2), ¬¬A→A=(-∞,1)∪(1,∞) ne ℝ."
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      "glosses": [
        "The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A."
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        "(logic) The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A."
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        "Double negative elimination"
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  "word": "law of double negation"
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      "examples": [
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          "text": "The law of double negation is not valid intuitionistically. To show this with Heyting algebra semantics, let A=(0,1)∪(1,2). Then ¬A=(-∞,0)∪(2,∞), ¬¬A=(0,2), ¬¬A→A=(-∞,1)∪(1,∞) ne ℝ."
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      "glosses": [
        "The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A."
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        "(logic) The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A."
      ],
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