reserve AS for AffinSpace;
reserve a,b,c,d,a9,b9,c9,d9,p,q,r,x,y for Element of AS;
reserve A,C,K,M,N,P,Q,X,Y,Z for Subset of AS;

theorem Th3:
  (a,b // A or b,a // A) & A // K implies a,b // K & b,a // K
proof
  assume that
A1: a,b // A or b,a // A and
A2: A // K;
  a,b // A by A1,AFF_1:34;
  hence a,b // K by A2,AFF_1:43;
  hence thesis by AFF_1:34;
end;
