reserve i,j for Nat;
reserve i,j for Nat,
  x for variable,
  l for quasi-loci;
reserve C for initialized ConstructorSignature,
  c for constructor OperSymbol of C;
reserve a,a9 for quasi-adjective,
  t,t1,t2 for quasi-term,
  T for quasi-type,

  c for Element of Constructors;

theorem
  for m being nullary OperSymbol of MaxConstrSign holds
  main-constr (m term) = m
  proof set C = MaxConstrSign;
    let m be nullary OperSymbol of C;
    the_arity_of m = 0 by Def13; then
    len the_arity_of m = 0 & len {} = 0; then
A1: m term = [m, the carrier of C]-tree {} &
    m-trm(<*>QuasiTerms C) = [m, the carrier of C]-tree {}
    by ABCMIZ_1:def 29,def 35;
    hence main-constr (m term) = ((m term).{})`1 by Def9
    .= [m, the carrier of C]`1 by A1,TREES_4:def 4
    .= m;
  end;
