reserve G for Robbins join-associative join-commutative non empty
  ComplLLattStr;
reserve x, y, z, u, v for Element of G;

theorem Th61:
  for L being Huntington de_Morgan preOrthoLattice holds Bot L = Bottom L
proof
  let L be Huntington de_Morgan preOrthoLattice;
  reconsider C = Bot L as Element of L;
A1: for a being Element of L holds C "/\" a = C & a "/\" C = C
  proof
    let a be Element of L;
    reconsider a9 = a as Element of L;
    thus C "/\" a = Bot L *' a9 by Def23
      .= C by Def9;
    hence thesis;
  end;
  then L is lower-bounded;
  hence thesis by A1,LATTICES:def 16;
end;
