reserve IPP for IncProjSp;
reserve a,b,c,d,p,q,o,r,s,t,u,v,w,x,y for POINT of IPP;
reserve A,B,C,D,L,P,Q,S for LINE of IPP;

theorem Th10:
  o on A & o on B & A<>B & a on A & o<>a & b on B & c on B & b<>c
  & a on P & b on P & c on Q implies P<>Q
proof
  assume that
A1: o on A & o on B & A<>B & a on A & o<>a and
A2: b on B & c on B & b<>c and
A3: a on P and
A4: b on P & c on Q;
  assume not thesis;
  then P=B by A2,A4,INCPROJ:def 4;
  hence contradiction by A1,A3,INCPROJ:def 4;
end;
