reserve n for non zero Element of NAT;
reserve a,b,r,t for Real;
reserve
  Z for open Subset of REAL,
 y0 for VECTOR of REAL-NS n,
  G for Function of REAL-NS n,REAL-NS n;

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;
