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 implies ex P st for Q holds {A,B,C} on Q iff P = Q
proof
  assume
A1: not {A,B,C} is linear;
  consider P such that
A2: {A,B,C} on P by Def12;
  take P;
  thus thesis by A1,A2,Def13;
end;
