for b1 being Nat holds not ( ex b2 being Nat st ( b2divides b1 & 1 < b2 & b2< b1 ) & ( for b2 being Nat holds not ( b2divides b1 & 1 < b2 & b2* b2<= b1 ) ) )
for b1 being Nat holds ( not ( not b1 is prime & not b1<= 1 & ( for b2 being Nat holds not ( b2divides b1 & 1 < b2 & b2< b1 ) ) ) & not ( not ( not b1<= 1 & ( for b2 being Nat holds not ( b2divides b1 & 1 < b2 & b2< b1 ) ) ) & b1 is prime ) )
Lemma14:
for b1 being Nat holds ( not ( not b1 is prime & not b1<= 1 & ( for b2 being Nat holds not ( b2divides b1 & 1 < b2 & b2* b2<= b1 & b2 is prime ) ) ) & not ( not ( not b1<= 1 & ( for b2 being Nat holds not ( b2divides b1 & 1 < b2 & b2* b2<= b1 & b2 is prime ) ) ) & b1 is prime ) )
for b1 being Prime for b2 being Nat for b3 being set holds not ( b2<> 0 & b3= b1|^(b1|-count b2) & ( for b4 being Nat holds not ( b4= b3 & 1 <= b4 & b4<= b2 ) ) )
Lemma33:
for b1 being Nat holds not ( 1 < b1 & b1< 29 & b1 is prime & not b1= 2 & not b1= 3 & not b1= 5 & not b1= 7 & not b1= 11 & not b1= 13 & not b1= 17 & not b1= 19 & not b1= 23 )
Lemma34:
for b1 being Nat holds ( b1< 841 implies for b2 being Nat holds not ( 1 < b2 & b2* b2<= b1 & b2 is prime & not b2= 2 & not b2= 3 & not b2= 5 & not b2= 7 & not b2= 11 & not b2= 13 & not b2= 17 & not b2= 19 & not b2= 23 ) )
for b1, b2 being Nat for b3 being Real for b4 being finiteset holds ( b4={ F1(b5,b2) where B is Prime : ( b5<= b3 & P1[b5,b2] ) } & b3>= 0 implies card b4<=[\b3/] )