Sentence examples for correctness follows from inspiring English sources

Their correctness follows directly from Theorem 4.2.

The correctness follows from preserving the invariants in all cases.

The runtime of this algorithm is in O(| E|log| V|) as for the original Kruskal algorithm and its correctness follows from the work of Carroll (1995).

The correctness of algorithm GraphConvergenceTree follows from the following lemma showing that every round roughly halves the distance between any two vertices, hence implying that the algorithm satisfies the agreement property.

The correctness of the algorithm follows from the correctness of the recursive equations, and can be asserted similarly as done for Algorithm 2. Assume for simplicity that compressed forms of both input strings s and t have the same length ñ.

They are summarized as follows: Correctness: VAO ≧ 3D > 2D.

The correctness of (3.8) follows directly from Theorem 2.4.

If (3) or (4) is correct, then by Theorem 3.1 there follows the correctness of the corresponding integral Hardy inequality (see [1]).

The correctness of Algorithm 1 follows directly from the relation given in Eq.  1 and the correctness of the tests performed in lines 11 and 19.

Correctness of this algorithm follows from the fact that through the whole algorithm we have and for.

The correctness of this procedure follows straightforwardly from the global version of Menger's theorem.