let k be Element of NAT ; :: thesis: ( k <> 0 implies 0 block k = 0 )
assume A1: k <> 0 ; :: thesis: 0 block k = 0
set F = { f where f is Function of 0 ,k : ( f is onto & f is "increasing ) } ;
{ f where f is Function of 0 ,k : ( f is onto & f is "increasing ) } = {}

proof

assume { f where f is Function of 0 ,k : ( f is onto & f is "increasing ) } <> {} ; :: thesis: contradiction
then consider x being set such that
A2: x in { f where f is Function of 0 ,k : ( f is onto & f is "increasing ) } by XBOOLE_0:def 1;
consider f being Function of 0 ,k such that
A3: ( x = f & f is onto & f is "increasing ) by A2;
thus contradiction by A1, A3, Def1; :: thesis: verum

end;

hence 0 block k = 0 ; :: thesis: verum