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 Th41:
  A // C implies C // A
proof
  assume A // C;
  then consider a,b,c,d such that
A1: a<>b and
A2: c <>d and
A3: a,b // c,d and
A4: A=Line(a,b) and
A5: C=Line(c,d) by Th36;
  c,d // a,b by A3,Th3;
  hence thesis by A1,A2,A4,A5,Th36;
end;
