theorem Th58:
  b,c _|_ a,a & a,a _|_ b,c & b,c // a,a & a,a // b,c
proof
  reconsider a9=a,b9=b,c9=c as Element of the AffinStruct of POS;
  thus b,c _|_ a,a by Def7;
  hence a,a _|_ b,c by Def7;
  b9,c9 // a9,a9 & a9,a9 // b9,c9 by AFF_1:3;
  hence thesis by Th36;
end;
