reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;
reserve i,j for Nat;
reserve F for Function,
  e,x,y,z for object;
reserve a,b,c for set;

theorem Th117:
  dom(a followed_by b) = NAT
proof
  thus dom(a followed_by b) = dom((NAT --> b) +* (0,a))
    .= dom(NAT --> b) by Th29
    .= NAT;
end;
