theorem Th71:
  for S being (11,1,1)-array non empty non void BoolSignature
  for J,L being set, K being SortSymbol of S
  st (the connectives of S).11 is_of_type <*J,L*>, K
  holds J = the_array_sort_of S &
  for I being integer SortSymbol of S holds the_array_sort_of S <> I
  proof
    let S be (11,1,1)-array non empty non void BoolSignature;
    let J0,L0 be set, K0 be SortSymbol of S;
    assume A1: (the connectives of S).11 is_of_type <*J0,L0*>, K0;
    consider J,K,L being Element of S such that
A2: L = 1 & K = 1 & J <> L & J <> K &
    (the connectives of S).11 is_of_type <*J,K*>, L &
    (the connectives of S).(11+1) is_of_type <*J,K,L*>, J &
    (the connectives of S).(11+2) is_of_type <*J*>, K &
    (the connectives of S).(11+3) is_of_type <*K,L*>, J by AOFA_A00:def 51;
A3: the_array_sort_of S = J by A2;
    thus J0 = <*J0,L0*>.1
    .= (the Arity of S).((the connectives of S).11).1 by A1
    .= <*J,K*>.1 by A2
    .= the_array_sort_of S by A3;
    thus thesis by A2,AOFA_A00:def 40;
  end;
