reserve n,m,k,k1,k2,i,j for Nat;
reserve x,y,z for object,X,Y,Z for set;
reserve A for Subset of X;
reserve B,A1,A2,A3 for SetSequence of X;
reserve Si for SigmaField of X;
reserve S,S1,S2,S3 for SetSequence of Si;

theorem
  Complement superior_setsequence B = inferior_setsequence Complement B
proof
  reconsider A2 = inferior_setsequence Complement B as SetSequence of X;
  Complement A2 = superior_setsequence Complement Complement B by Th32
    .= superior_setsequence B;
  hence thesis;
end;
