reserve s for set,
  i,j for natural Number,
  k for Nat,
  x,x1,x2,x3 for Real,
  r,r1,r2,r3,r4 for Real,
  F,F1,F2,F3 for real-valued FinSequence,
  R,R1,R2 for Element of i-tuples_on REAL;
reserve z,z1,z2 for Element of COMPLEX;
reserve n for Nat,
  x, y, a for Real,
  p, p1, p2, p3, q, q1, q2 for Element of n-tuples_on REAL;
reserve f,g for real-valued FinSequence;

theorem Th143:
  len f = len sqr f & dom f = dom sqr f
proof
  rng f c= REAL & dom sqrreal = REAL by FUNCT_2:def 1;
  hence len f = len (sqrreal*f) by FINSEQ_2:29
    .= len sqr f;
  hence thesis by FINSEQ_3:29;
end;
