reserve i,j,k,k1,k2,n,m,i1,i2,j1,j2 for Element of NAT,
  x for set;

theorem Th3:
  for i1,i2,j1,j2 being Nat st i1,j1,i2,j2 are_adjacent holds
  i1+1,j1+1,i2+1,j2+1 are_adjacent
proof
  let i1,i2,j1,j2 be Nat;
  assume i1,j1,i2,j2 are_adjacent;
  then i1,i2 are_adjacent & j1=j2 or i1=i2 & j1,j2 are_adjacent;
  then i1+1,i2+1 are_adjacent & j1+1=j2+1 or i1+1=i2+1 & j1+1,j2+1
  are_adjacent;
  hence thesis;
end;
