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 Th59:
  for X being finite Subset of Vars st varcl X = X
  for s being SortSymbol of MaxConstrSign
  ex m being constructor OperSymbol of s st ::a_Type MaxConstrSign
  ex p being FinSequence of QuasiTerms MaxConstrSign
  st len p = len the_arity_of m & vars (m-trm p) = X
  proof
    let X be finite Subset of Vars;
    assume
A1: varcl X = X; then
    consider l such that
A2: rng l = X by Th31;
    set n = len l;
    set C = MaxConstrSign;
    let s be SortSymbol of C;
    consider m being constructor OperSymbol of s such that
A3: len the_arity_of m = n by Th57;
    take m;
    set p = args l;
    take p;
    thus len p = len the_arity_of m by A3,Def18;
    thus thesis by A1,A2,A3,Th58;
  end;
