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 unary constructor OperSymbol of MaxConstrSign
  for t holds main-constr (m term t) = m
  proof set C = MaxConstrSign;
    let m be unary constructor OperSymbol of C;
    let t;
    reconsider w = t as Element of QuasiTerms C by ABCMIZ_1:49;
    reconsider p = <*w*> as FinSequence of QuasiTerms C;
A1: len the_arity_of m = 1 by Def14; then
    the_arity_of m = 1 |-> a_Term by ABCMIZ_1:37
    .= <*a_Term*> by FINSEQ_2:59; then
    len p = 1 & (the_arity_of m).1 = a_Term C by FINSEQ_1:40; then
A2: m term t = [m, the carrier of C]-tree <*t*> &
    m-trm p = [m, the carrier of C]-tree <*t*> by A1,ABCMIZ_1:def 30,def 35;
    hence main-constr (m term t) = ((m term t).{})`1 by Def9
    .= [m, the carrier of C]`1 by A2,TREES_4:def 4
    .= m;
  end;
