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 Th59:
  for f st ColVec2Mx f in Solutions_of(A,ColVec2Mx b) holds len f = width A
proof
  let f;
  assume ColVec2Mx f in Solutions_of(A,ColVec2Mx b);
  then
A1: ex g st ColVec2Mx f = ColVec2Mx g & len g = width A by Th58;
  len ColVec2Mx f = len f by MATRIX_0:def 2;
  hence thesis by A1,MATRIX_0:def 2;
end;
