reserve n,k for Element of NAT;

theorem Th10:
  for L be LATTICE for x be Element of L holds x in Join-IRR L iff
  x<>Bottom L & for b,c be Element of L holds x= b"\/"c implies x=b or x=c
proof
  let L be LATTICE;
  let x be Element of L;
  thus x in Join-IRR L implies x <> Bottom L & for b,c be Element of L holds x
  = b"\/"c implies x=b or x=c
  proof
    assume x in Join-IRR L;
    then
    ex a being Element of L st x = a & a<>Bottom L & for b,c be Element of
    L holds a= b"\/"c implies a=b or a=c;
    hence thesis;
  end;
  thus thesis;
end;
