take 1 ; :: according to ASYMPT_0:def 4 :: thesis: for b₁ being set holds
( not 1 <= b₁ or not (seq_n^ a) . b₁ <= 0 )
set f = seq_n^ a;
let n be Nat; :: thesis: ( not 1 <= n or not (seq_n^ a) . n <= 0 )
A1: n in NAT by ORDINAL1:def 12;
assume A2: n >= 1 ; :: thesis: not (seq_n^ a) . n <= 0
then (seq_n^ a) . n = n to_power a by Def3, A1;
hence not (seq_n^ a) . n <= 0 by A2, POWER:34; :: thesis: verum