corollary

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theorem

theorem, in mathematics and logic, statement in words or symbols that can be established by means of deductive logic; it differs from an axiom in that a proof is required for its acceptance. A lemma is a theorem that is demonstrated as an intermediate step in the proof of another, more basic theorem. A corollary is a theorem that follows as a direct consequence of another theorem or an axiom. There are many famous theorems in mathematics, often known by the name of their discoverer, e.g., the Pythagorean Theorem, concerning right triangles. One of the most famous problems of number theory was the proof of Fermat's Last Theorem (see Fermat, Pierre de); the theorem states that for an integer n greater than 2 the equation xn+yn=zn admits no solutions where x, y, and z are also integers.
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corollary

Logic a proposition that follows directly from the proof of another proposition
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
Applying this remark to Corollaries 4, 5, 8, and 9, respectively, we obtain following results.
In Corollaries 4.8 and 4.12 we saw for primitives that if (m, n) [??] F(F) [union] {n}, then N([F.sup.m]) = N(F).
Hence, if a < 8/104,2912 holds, then the conditions of Corollaries 3 and 4 are satisfied.
By the similar reasons used in the case of modular, we obtain the following corollaries immediately.
Taking [a.sub.1] = a, [a.sub.r] = b in Theorem 2 we obtain the following corollaries:
At the same time, we can get the following corollaries. The proof for corollaries is similar to that in large-scale Lurie systems with single nonlinearity and thus is omitted.
On the other hand, by Theorem 42, we will also obtain the following corollaries.
Note that for [alpha] = 1, the above three corollaries reduce to the results of Singh and Gupta.
We also have the following corollaries of Theorem 3.1.
Although this rule needs no further clarification, that didn't stop Igor from adding 2 corollaries:
Similarly to Corollaries 2.2 and 2.3 the following corollaries hold.
In particular, we obtain the following corollaries.