
theorem Th30:
  for L being non empty OrthoLattStr st L is Boolean
  well-complemented Lattice-like holds L is Ortholattice
proof
  let L be non empty OrthoLattStr;
  assume L is Boolean well-complemented Lattice-like;
  then reconsider L9 = L as Boolean well-complemented Lattice-like non empty
  OrthoLattStr;
A1: for x, y being Element of L9 holds x "/\" y = (x` "\/" y`)` by ROBBINS1:33;
  ( for x being Element of L9 holds x`` = x)& for x, y being Element of L9
  holds x |_| x` = y |_| y` by ROBBINS1:3,4;
  hence thesis by A1,Def6,Def7,ROBBINS1:def 23;
end;
