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;

theorem Th35:
  for c being constructor OperSymbol of C
  for p being FinSequence of QuasiTerms C st len p = len the_arity_of c
  holds main-constr (c-trm p) = c
  proof
    let c be constructor OperSymbol of C;
    let p be FinSequence of QuasiTerms C;
    assume len p = len the_arity_of c; then
    c-trm p = [c, the carrier of C]-tree p by ABCMIZ_1:def 35; then
    (c-trm p).{} = [c, the carrier of C] by TREES_4:def 4;
    hence main-constr (c-trm p) = [c, the carrier of C]`1 by Def9
    .= c;
  end;
