set X = { k where k is Nat : ( k mod m = r & k divides n ) } ;
{ k where k is Nat : ( k mod m = r & k divides n ) } c= NAT

proof

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in { k where k is Nat : ( k mod m = r & k divides n ) } or x in NAT )
assume x in { k where k is Nat : ( k mod m = r & k divides n ) } ; :: thesis: x in NAT
then ex k being Nat st
( x = k & k mod m = r & k divides n ) ;
hence x in NAT by ORDINAL1:def 12; :: thesis: verum

end;

hence { k where k is Nat : ( k mod m = r & k divides n ) } is Subset of NAT ; :: thesis: verum