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

proof

assume { f where f is Function of (Segm n),(Segm 0) : ( f is onto & f is "increasing ) } <> {} ; :: thesis: contradiction
then consider x being object such that
A2: x in { f where f is Function of (Segm n),(Segm 0) : ( f is onto & f is "increasing ) } by XBOOLE_0:def 1;
ex f being Function of (Segm n),(Segm 0) st
( x = f & f is onto & f is "increasing ) by A2;
hence contradiction by A1; :: thesis: verum

end;

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