reserve k,t,i,j,m,n for Nat,
  x,y,y1,y2 for object,
  D for non empty set;

theorem Th3:
  for M be Matrix of n+1,m,D holds Del(M,n+1) is Matrix of n,m,D
proof
  let M be Matrix of n+1,m,D;
A1: len M = n + 1 by MATRIX_0:def 2;
  then
A2: len Del(M,n+1) = n by Th1;
  per cases;
  suppose
A3: n = 0;
    then Del(M,n+1) = {} by A2;
    hence thesis by A3,MATRIX_0:13;
  end;
  suppose
A4: n > 0;
    width M = m by A1,MATRIX_0:20;
    then width Del(M,n+1) = m by A4,Th2;
    hence thesis by A2,A4,MATRIX_0:20;
  end;
