theorem
  E is_space3 implies ex a,b,c,d st not a,b,c,d are_coplanar &
  E = space3(a,b,c,d)
  proof
    assume E is_space3;
    then consider r be POINT of S, A be Subset of S such that
A1: A is_plane and
A2: not r in A and
A3: E = space3(A,r);
    consider a,b,c be POINT of S such that
A4: not Collinear a,b,c and
A5: A = Plane(a,b,c) by A1;
    take a,b,c,r;
    a in A & b in A & c in A by A4,A5,Th69;
    hence thesis by A5,A3,Def21,A1,A2,A4,Th87;
  end;
