reserve x,N for set,
        k for Nat;
reserve N for with_zero set;
reserve S for IC-Ins-separated non empty with_non-empty_values
     Mem-Struct over N;
reserve s for State of S;
reserve p for PartState of S;

theorem
 for s being State of S st IC s =  0 holds Initialize s = s
proof let s be State of S;
  IC S in dom s by Th2;
  hence thesis by FUNCT_7:96;
end;
