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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