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 Th75:
 for S be with_non-empty_values Mem-Struct over N
 for p being FinPartState of S holds p in FinPartSt S
proof
  let S be with_non-empty_values Mem-Struct over N;
  let p be FinPartState of S;
   p in sproduct the_Values_of S by CARD_3:103;
  hence thesis;
end;
