
theorem
  for C being FormalContext holds "\/"([#] the carrier of ConceptLattice
(C),C) = Concept-with-all-Objects(C) & "/\"([#] the carrier of ConceptLattice(C
  ),C) = Concept-with-all-Attributes(C)
proof
  let C be FormalContext;
A1: @Concept-with-all-Attributes(C) is_less_than [#] the carrier of
  ConceptLattice(C)
  proof
    let q be Element of ConceptLattice(C);
    assume q in [#] the carrier of ConceptLattice(C);
    Concept-with-all-Attributes(C) is-SubConcept-of q@ &
Concept-with-all-Attributes(C) = (@Concept-with-all-Attributes(C))@ by
CONLAT_1:30,def 21;
    hence thesis by CONLAT_1:43;
  end;
  "\/"(the carrier of ConceptLattice(C),ConceptLattice(C)) = Top
ConceptLattice (C) & for b being Element of ConceptLattice(C) st b is_less_than
[#] the carrier of ConceptLattice(C) holds b [= @Concept-with-all-Attributes(C)
  by LATTICE3:50;
  hence thesis by A1,Th1,LATTICE3:34;
end;
