theorem
  for L being strict Lattice holds latt <.L.) = L
proof
  let L be strict Lattice;
  dom the L_meet of L = [:the carrier of L, the carrier of L:] by FUNCT_2:def 1
;
  then
A1: the L_meet of L = (the L_meet of L)||the carrier of L by RELAT_1:68;
  dom the L_join of L = [:the carrier of L, the carrier of L:] by FUNCT_2:def 1
;
  then the L_join of L = (the L_join of L)||the carrier of L by RELAT_1:68;
  hence thesis by A1,Def9;
end;
