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 dilatation implies for a,b,c
  holds LIN a,b,c iff LIN f.a,f.b,f.c
proof
  assume
A1: f is dilatation;
  let a,b,c;
  a,b // a,c iff f.a,f.b // f.a,f.c by A1,Th72;
  hence thesis by AFF_1:def 1;
end;
