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
  not {A,B,C} is linear & D on Plane(A,B,C) implies {A,B,C,D} is planar
proof
  assume that
A1: not {A,B,C} is linear and
A2: D on Plane(A,B,C);
  {A,B,C} on Plane(A,B,C) by A1,Def20;
  then {A,B,C} \/ {D} on Plane(A,B,C) by A2,Th9;
  then {A,B,C,D} on Plane(A,B,C) by ENUMSET1:6;
  hence thesis;
end;
