reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;
reserve D for set;
reserve i for Nat;
reserve m for Nat,
        D for non empty set;

theorem
 for F being finite initial NAT-defined Function
 for n being Nat holds
  n in dom F iff n < card F by Lm1;
