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 Th62:
 k in dom G implies Line(DelCol(G,i),k) = Del(Line(G,k),i)
proof
  set D = DelCol(G,i);
  assume that
A1: k in dom G;
  len D = len G by Def13;
  then
A2: dom D = dom G by FINSEQ_3:29;
  D.k = Del(Line(G,k),i) by A1,Def13;
  hence thesis by A1,A2,Th60;
end;
