reserve a,b,c,d,e,f for Real,
        g           for positive Real,
        x,y         for Complex,
        S,T         for Element of REAL 2,
        u,v,w       for Element of TOP-REAL 3;
reserve a,b,c for Element of F_Real,
          M,N for Matrix of 3,F_Real;
reserve D        for non empty set;
reserve d1,d2,d3 for Element of D;
reserve A        for Matrix of 1,3,D;
reserve B        for Matrix of 3,1,D;

theorem Th23:
  (A@) is (3,1)-size
  proof
    width A = 3 & len A = 1 by MATRIX_0:23; then
A1: len (A@) = 3 & width (A@) = 1 by MATRIX_0:29;
    then consider s1 be FinSequence such that
A2: s1 in rng (A@) and
A3: len s1 = 1 by MATRIX_0:def 3;
    consider n0 be Nat such that
A4: for x be object st x in rng (A@) holds ex s be FinSequence st s = x &
    len s = n0 by MATRIX_0:def 1;
    consider s be FinSequence such that
A5: s = s1 and
A6: len s = n0 by A2,A4;
    for p be FinSequence of D st p in rng (A@) holds len p = 1
    proof
      let p be FinSequence of D;
      assume
A7:   p in rng (A@);
      consider s be FinSequence such that
A8:   s = p and
A9:   len s = n0 by A7,A4;
      thus thesis by A3,A5,A6,A8,A9;
    end;
    hence thesis by A1,MATRIX_0:def 2;
  end;
