reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;
reserve C for initialized ConstructorSignature,
  s for SortSymbol of C,
  o for OperSymbol of C,
  c for constructor OperSymbol of C;
reserve a,b for expression of C, an_Adj C;
reserve t, t1,t2 for expression of C, a_Type C;

theorem Th46:
  (ast C)term(a,t) is expression of C, a_Type C &
  (ast C)term(a,t) = [ *, the carrier of C]-tree <*a,t*>
proof
A1: the_result_sort_of ast C = a_Type C by Def9;
A2: the_arity_of ast C = <*an_Adj C, a_Type C*> by Def9;
  then
A3: len the_arity_of ast C = 2 by FINSEQ_1:44;
A4: (the_arity_of ast C).1 = an_Adj C by A2;
A5: (the_arity_of ast C).2 = a_Type C by A2;
  then (ast C)term(a,t) = [ *, the carrier of C]-tree <*a,t*> by A3,A4,Def31;
  hence thesis by A1,A3,A4,A5,Th45;
end;
