let a be positive Real; :: thesis: seq_a^ (a,1,0) is positive

now :: thesis: for n being Nat holds 0 < (seq_a^ (a,1,0)) . n

let n be Nat; :: thesis: 0 < (seq_a^ (a,1,0)) . n
(seq_a^ (a,1,0)) . n = a to_power ((1 * n) + 0) by ASYMPT_1:def 1
.= a to_power n ;
hence 0 < (seq_a^ (a,1,0)) . n by POWER:34; :: thesis: verum

end;

hence seq_a^ (a,1,0) is positive ; :: thesis: verum