reserve AP for AffinPlane,
  a,a9,b,b9,c,c9,x,y,o,p,q,r,s for Element of AP,
  A,C,C9,D,K,M,N,P,T for Subset of AP;

theorem
  AP is Desarguesian implies AP is Moufangian
proof
  assume
A1: AP is Desarguesian;
    let K,o,a,b,c,a9,b9,c9;
    assume that
A2: K is being_line and
A3: o in K and
A4: c in K & c9 in K and
A5: not a in K and
A6: o<>c and
A7: a<>b and
A8: LIN o,a,a9 and
A9: LIN o,b,b9 and
A10: a,b // a9,b9 & a,c // a9,c9 and
A11: a,b // K;
    set A=Line(o,a), P=Line(o,b);
A12: o in A by A3,A5,AFF_1:24;
A13: now
      assume
A14:  o=b;
      b,a // K by A11,AFF_1:34;
      hence contradiction by A2,A3,A5,A14,AFF_1:23;
    end;
    then
A15: b in P by AFF_1:24;
A16: a in A by A3,A5,AFF_1:24;
A17: A is being_line by A3,A5,AFF_1:24;
A18: A<>P
    proof
      assume A=P;
      then a,b // A by A17,A16,A15,AFF_1:40,41;
      hence contradiction by A3,A5,A7,A11,A12,A16,AFF_1:45,53;
    end;
A19: P is being_line & o in P by A13,AFF_1:24;
    then
A20: b9 in P by A9,A13,A15,AFF_1:25;
    a9 in A by A3,A5,A8,A17,A12,A16,AFF_1:25;
    hence thesis by A1,A2,A3,A4,A5,A6,A10,A13,A17,A12,A16,A19,A15,A20,A18;
end;
