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 Th19:
  not {A,B,C} is linear & {A,B,C} on P & not D on P implies not {A
  ,B,C,D} is planar
proof
  assume that
A1: ( not {A,B,C} is linear)& {A,B,C} on P and
A2: not D on P;
  given Q such that
A3: {A,B,C,D} on Q;
  {A,B,C} \/ {D} on Q by A3,ENUMSET1:6;
  then {A,B,C} on Q by Th9;
  then P = Q by A1,Def13;
  hence contradiction by A2,A3,Th5;
end;
