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# Difference between revisions of "Proof (mathematics)"

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In [[mathematics]], a '''proof''' of a statement | In [[mathematics]], a '''proof''' of a statement | ||

− | (called theorem, proposition, lemma, etc. according to the context and its importance) | + | (called [[theorem]], [[proposition]], [[lemma]], etc. according to the context and its importance) |

is a series of arguments which show that the assumptions of the statement imply its conclusion. | is a series of arguments which show that the assumptions of the statement imply its conclusion. | ||

Besides the assumptions listed explicitely in the statement to be proven, | Besides the assumptions listed explicitely in the statement to be proven, | ||

the arguments — which have to be based on inference rules of mathematical logic — | the arguments — which have to be based on inference rules of mathematical logic — | ||

may use the axioms of the theory and previously proven statements. | may use the axioms of the theory and previously proven statements. |

## Latest revision as of 21:09, 12 August 2020

In mathematics, a **proof** of a statement
(called theorem, proposition, lemma, etc. according to the context and its importance)
is a series of arguments which show that the assumptions of the statement imply its conclusion.
Besides the assumptions listed explicitely in the statement to be proven,
the arguments — which have to be based on inference rules of mathematical logic —
may use the axioms of the theory and previously proven statements.