reserve AS for AffinSpace;
reserve a,a9,b,b9,c,d,o,p,q,r,s,x,y,z,t,u,w for Element of AS;
reserve A,C,D,K for Subset of AS;

theorem Th16:
  c in Line(a,b) & d in Line(a,b) & a<>b implies Line(a,b) c= Line (c,d)
proof
  assume that
A1: c in Line(a,b) and
A2: d in Line(a,b) and
A3: a<>b;
A4: LIN a,b,d by A2,Def2;
A5: LIN a,b,c by A1,Def2;
    let x be object;
    assume
A6: x in Line(a,b);
    then reconsider x9=x as Element of AS;
    LIN a,b,x9 by A6,Def2;
    then LIN c,d,x9 by A3,A5,A4,Th7;
    hence x in Line(c,d) by Def2;
end;
