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
  A <> B implies ex L st for K holds {A,B} on K iff K = L
proof
  assume
A1: A <> B;
  consider L such that
A2: {A,B} on L by Def9;
  take L;
  thus thesis by A1,A2,Def10;
end;
