theorem
  L is lower-bounded implies latt (L,I) is lower-bounded
proof
  set b9 = the Element of latt (L,I);
  reconsider b = b9 as Element of L by Th68;
  given c being Element of L such that
A1: for a being Element of L holds c"/\"a = c & a"/\"c = c;
A2: carr(latt (L,I)) = I by Th72;
  c"/\"b = c by A1;
  then reconsider c9 = c as Element of latt (L,I) by A2,Th22;
  take c9;
  let a9 be Element of latt (L,I);
  reconsider a = a9 as Element of L by Th68;
  thus c9"/\"a9 = c"/\"a by Th73
    .= c9 by A1;
  hence a9"/\"c9 = c9;
end;
