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 Th120:
  dom (a,b) followed_by c = NAT
proof
  thus dom (a,b) followed_by c = dom(NAT --> c) \/ dom (0,1) --> (a,b) by
FUNCT_4:def 1
    .= NAT \/ dom (0,1) --> (a,b)
    .= NAT \/ {0,1} by FUNCT_4:62
    .= NAT by XBOOLE_1:12;
end;
