reserve a,b,p,k,l,m,n,s,h,i,j,t,i1,i2 for natural Number;

theorem Th52:
  i-'k <= j implies i <= j + k
proof
  assume
A1: i-'k <= j;
  per cases;
  suppose
A2: i >= k;
    i-'k +k <= j + k by A1,XREAL_1:6;
    hence thesis by A2,XREAL_1:235;
  end;
  suppose
A3: i <= k;
    k <= j + k by NAT_1:11;
    hence thesis by A3,XXREAL_0:2;
  end;
end;
