reserve x,y,z for object,
  i,j,n,m for Nat,
  D for non empty set,
  s,t for FinSequence,
  a,a1,a2,b1,b2,d for Element of D,
  p, p1,p2,q,r for FinSequence of D;
reserve M,M1,M2 for Matrix of D;
reserve f for FinSequence of D;
reserve i,j,i1,j1 for Nat;
reserve k for Nat, G for Matrix of D;
reserve x,y,x1,x2,y1,y2 for object,
  i,j,k,l,n,m for Nat,
  D for non empty set,
  s,s2 for FinSequence,
  a,b,c,d for Element of D,
  q,r for FinSequence of D,
  a9,b9 for Element of D;

theorem
 width G > 1 & i in Seg width G implies DelCol(G,i) is not empty-yielding
proof assume that
A1: width G > 1 and
A2:i in Seg width G;
  width DelCol(G,i)+1 > 0+1 by A1,A2,Th64;
  then
A3: width DelCol(G,i) > 0;
  then len DelCol(G,i) > 0 by Def3;
 hence DelCol(G,i) is not empty-yielding by A3;
end;
