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 q being expression of MaxConstrSign, a_Type MaxConstrSign
  for a holds main-constr ((ast MaxConstrSign)term(a,q)) = *
  proof set C = MaxConstrSign;
    set m = ast C;
    let q be expression of MaxConstrSign, a_Type MaxConstrSign;
    let a;
A1: len the_arity_of m = 2 by Def15;
    the_arity_of m = <*an_Adj C,a_Type C*> by ABCMIZ_1:38; then
    (the_arity_of m).1 = an_Adj C & (the_arity_of m).2 = a_Type C; then
A2: m term(a,q) = [m, the carrier of C]-tree <*a,q*> by A1,ABCMIZ_1:def 31;
    thus main-constr (m term(a,q)) = ((m term(a,q)).{})`1 by Def9
    .= [m, the carrier of C]`1 by A2,TREES_4:def 4
    .= *;
  end;
