
theorem
  for C being FormalContext holds "\/"({} ConceptLattice(C),C) =
  Concept-with-all-Attributes(C) & "/\"({} ConceptLattice(C),C) =
  Concept-with-all-Objects(C)
proof
  let C be FormalContext;
A1: for b being Element of ConceptLattice(C) st b is_less_than {} holds b [=
  @Concept-with-all-Objects(C)
  proof
    let b be Element of ConceptLattice(C);
    assume b is_less_than {};
    b@ is-SubConcept-of Concept-with-all-Objects(C) &
Concept-with-all-Objects(C ) = (@Concept-with-all-Objects(C))@ by CONLAT_1:30
,def 21;
    hence thesis by CONLAT_1:43;
  end;
  "\/"({} ConceptLattice(C),C) = Bottom ConceptLattice(C) & @
  Concept-with-all-Objects(C) is_less_than {} by LATTICE3:49;
  hence thesis by A1,Th1,LATTICE3:34;
end;
