Conditional proofs are of great importance in mathematics.
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A famous network of conditional proofs is the NP-complete class of complexity theory.
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Such sentences are called conditional sentences, and the standard method for proving them is called conditional proof.
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The Hooley published a conditional proof for the second conjecture, assuming certain cases of the Generalized Riemann hypothesis.
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The assumed antecedent of a conditional proof is called the " conditional proof assumption " ( CPA ).
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The assumed antecedent of a conditional proof is called the " conditional proof assumption " ( CPA ).
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In 1967, Hooley published a conditional proof for the conjecture, assuming certain cases of the Generalized Riemann hypothesis.
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Then negation introduction and elimination are just special cases of implication introduction ( conditional proof ) and elimination ( modus ponens ).
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Thus, the goal of a conditional proof is to demonstrate that if the CPA were true, then the desired conclusion necessarily follows.
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Conditional proofs exist linking several otherwise unproven conjectures, so that a proof of one conjecture may immediately imply the validity of several others.
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