reserve p,p1,p2,p3,p11,p22,q,q1,q2 for Point of TOP-REAL 2,
  f,h for FinSequence of TOP-REAL 2,
  r,r1,r2,s,s1,s2 for Real,
  u,u1,u2,u5 for Point of Euclid 2,
  n,m,i,j,k for Nat,
  N for Nat,
  x,y,z for set;

theorem Th5:
  p1=<*r1,s1*> & p2=<*r2,s2*> implies p1+p2=<*r1+r2,s1+s2*> & p1-
  p2=<*r1-r2,s1-s2*>
proof
A1: |[r1,s1]|`1=r1 & |[r1,s1]|`2=s1;
A2: |[r2,s2]|`1=r2 & |[r2,s2]|`2=s2;
  assume p1=<*r1,s1*> & p2=<*r2,s2*>;
  hence thesis by A1,A2,EUCLID:55,61;
end;
