
theorem
  for L be lower-bounded antisymmetric transitive with_infima
  with_suprema RelStr for a,b,c be Element of L holds a meets b"/\"c implies a
  meets b
proof
  let L be lower-bounded antisymmetric transitive with_infima with_suprema
  RelStr;
  let a,b,c be Element of L;
  assume
A1: a meets b"/\"c;
  assume
A2: not a meets b;
  a"/\"(b"/\"c)= (a"/\"b)"/\"c by LATTICE3:16
    .= Bottom L "/\"c by A2
    .= Bottom L by Th25;
  hence contradiction by A1;
end;
