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 Th17:
  A is being_line & C is being_line & a in A & b in A & a in C & b in C
  implies a=b or A=C
proof
  assume that
A1: A is being_line and
A2: C is being_line and
A3: a in A and
A4: b in A and
A5: a in C and
A6: b in C;
  assume
A7: a<>b;
  then A=Line(a,b) by A1,A3,A4,Lm6;
  hence thesis by A2,A5,A6,A7,Lm6;
end;
