reserve x,y for set,
  i,j,k,l,m,n for Nat,
  K for Field,
  N for without_zero finite Subset of NAT,
  a,b for Element of K,
  A,B,B1,B2,X,X1,X2 for (Matrix of K),
  A9 for (Matrix of m,n,K),
  B9 for (Matrix of m,k,K);
reserve D for non empty set,
  bD for FinSequence of D,
  b,f,g for FinSequence of K,
  MD for Matrix of D;

theorem Th33:
  Solutions_of(A,B) is non empty implies len A = len B
proof
  assume Solutions_of(A,B) is non empty;
  then consider x being object such that
A1: x in Solutions_of(A,B);
  ex X st X=x & len X= width A & width X = width B & A * X = B by A1;
  hence thesis by MATRIX_3:def 4;
end;
