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 Th7:
  (A // C or C // A) & a<>b & (a,b // c,d or c,d // a,b) & a in A &
  b in A & c in C implies d in C
proof
  assume that
A1: A // C or C // A and
A2: a<>b &( a,b // c,d or c,d // a,b) and
A3: a in A & b in A and
A4: c in C;
  A is being_line by A1,AFF_1:36;
  then a,b // A by A3,AFF_1:52;
  then c,d // A by A2,Th4;
  then c,d // C by A1,Th3;
  hence thesis by A4,Th2;
end;
