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 Th29:
  not {A,B,C} is linear implies Plane(A,B,C) = Plane(A,C,B)
proof
  assume
A1: not {A,B,C} is linear;
  then not {A,C,B} is linear by ENUMSET1:57;
  then {A,C,B} on Plane(A,C,B) by Def20;
  then {A,B,C} on Plane(A,C,B) by ENUMSET1:57;
  hence thesis by A1,Def20;
end;
