theorem Th53:
  a<b & G is_Lipschitzian_on the carrier of REAL-NS n implies
  Fredholm(G,a,b,y0) is with_unique_fixpoint
proof
  assume a<b & G is_Lipschitzian_on the carrier of REAL-NS n; then
  ex m be Nat st iter(Fredholm(G,a,b,y0),(m+1)) is contraction by Th52;
  hence thesis by Th7;
end;
