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;
reserve lambda for Real;
reserve f for FinSequence of REAL;

theorem Th45:
  len f = n implies f in the carrier of Euclid n
proof
 f in REAL* & n-tuples_on REAL = { s where s is Element of REAL*: len s =
  n } by FINSEQ_1:def 11,FINSEQ_2:def 4;
  hence thesis;
end;
