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 binary constructor OperSymbol of MaxConstrSign
  for t1,t2 holds main-constr (m term(t1,t2)) = m
  proof set C = MaxConstrSign;
    let m be binary constructor OperSymbol of C;
    let t1,t2;
    reconsider w1 = t1, w2 = t2 as Element of QuasiTerms C by ABCMIZ_1:49;
    reconsider p = <*w1,w2*> as FinSequence of QuasiTerms C;
A1: len the_arity_of m = 2 by Def15; then
    the_arity_of m = 2 |-> a_Term by ABCMIZ_1:37
    .= <*a_Term,a_Term*> by FINSEQ_2:61; then
    (the_arity_of m).1 = a_Term C & (the_arity_of m).2 = a_Term C & len p = 2
    by FINSEQ_1:44; then
A2: m term(t1,t2) = [m, the carrier of C]-tree <*t1,t2*> &
    m-trm p = [m, the carrier of C]-tree p by A1,ABCMIZ_1:def 31,def 35;
    hence main-constr (m term(t1,t2)) = ((m term(t1,t2)).{})`1 by Def9
    .= [m, the carrier of C]`1 by A2,TREES_4:def 4
    .= m;
  end;
