**Theorem Th5.6-1**

If for every pair of pointers *(i,j)** *there is the set of the non negative numbers *S(i,j)* and the set of
pointers *K(i,j)* in such a way that the *S(i,j)** *set is the union:

- S(i,j)=U{S(i,k)+S(k,j),k belonging to the K(i,j) set .}

then for the minimum element of the S(i,j) set :

- min S(i,j)=min{minS(i,k)+minS(k,j)},

and the proofing of this is quite easy.

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