reserve S for IncStruct;
reserve A,B,C,D for POINT of S;
reserve L for LINE of S;
reserve P for PLANE of S;
reserve F,G for Subset of the Points of S;
reserve a,b,c for Element of {0,1,2,3};
reserve S for IncSpace;
reserve A,B,C,D,E for POINT of S;
reserve K,L,L1,L2 for LINE of S;
reserve P,P1,P2,Q for PLANE of S;
reserve F for Subset of the Points of S;

theorem
  ex A st A on P & not A on L
proof
  consider A,B such that
A1: A <> B and
A2: {A,B} on L by Def8;
  consider C such that
A3: C on P and
A4: not {A,B,C} is linear by A1,Th44;
  take C;
  thus C on P by A3;
  C on L implies {A,B} \/ {C} on L by A2,Th8;
  then C on L implies {A,B,C} on L by ENUMSET1:3;
  hence thesis by A4;
end;
