reserve A for non empty set,
  a,b,x,y,z,t for Element of A,
  f,g,h for Permutation of A;
reserve R for Relation of [:A,A:];
reserve AS for non empty AffinStruct;
reserve a,b,x,y for Element of AS;
reserve CS for CongrSpace;
reserve OAS for OAffinSpace;
reserve a,b,c,d,p,q,r,x,y,z,t,u for Element of OAS;
reserve f,g for Permutation of the carrier of OAS;
reserve AFS for AffinSpace;
reserve a,b,c,d,d1,d2,p,x,y,z,t for Element of AFS;
reserve f,g for Permutation of the carrier of AFS;

theorem
  f is collineation & g is collineation implies f" is collineation & f*g
  is collineation & id the carrier of AFS is collineation
proof
  assume f is_automorphism_of the CONGR of AFS & g is_automorphism_of the
  CONGR of AFS;
  hence f" is_automorphism_of the CONGR of AFS & f*g is_automorphism_of the
  CONGR of AFS by Th17,Th18;
  thus id the carrier of AFS is_automorphism_of the CONGR of AFS;
end;
