take 0 ; :: according to ASYMPT_0:def 6 :: thesis: for b₁ being Element of NAT holds
( not 0 <= b₁ or not (seq_a^ (a,b,c)) . b₁ <= 0 )
set f = seq_a^ (a,b,c);
let n be Element of NAT ; :: thesis: ( not 0 <= n or not (seq_a^ (a,b,c)) . n <= 0 )
assume n >= 0 ; :: thesis: not (seq_a^ (a,b,c)) . n <= 0
(seq_a^ (a,b,c)) . n = a to_power ((b * n) + c) by Def1;
hence not (seq_a^ (a,b,c)) . n <= 0 by POWER:39; :: thesis: verum