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 P st A on P & not L on P
proof
  consider B such that
A1: A <> B and
A2: B on L by Lm1;
  consider C,D such that
A3: not {A,B,C,D} is planar by A1,Th47;
  take P = Plane(A,C,D);
A4: not {A,C,D,B} is planar by A3,ENUMSET1:63;
  then not {A,C,D} is linear by Th17;
  then
A5: {A,C,D} on P by Def20;
  hence A on P by Th4;
  B on P implies {A,C,D} \/ {B} on P by A5,Th9;
  then B on P implies {A,C,D,B} on P by ENUMSET1:6;
  hence thesis by A2,A4,Def17;
end;
