now :: thesis: for S being set st S in rng <*G,F*> holds
S is AbGroup

let S be set ; :: thesis: ( S in rng <*G,F*> implies S is AbGroup )
assume S in rng <*G,F*> ; :: thesis: S is AbGroup
then consider i being object such that
A1: ( i in dom <*G,F*> & <*G,F*> . i = S ) by FUNCT_1:def 3;
dom <*G,F*> = {1,2} by FINSEQ_1:2, FINSEQ_1:89;
then ( i = 1 or i = 2 ) by A1, TARSKI:def 2;
hence S is AbGroup by A1; :: thesis: verum

end;

hence for b₁ being FinSequence st b₁ = <*G,F*> holds
( not b₁ is empty & b₁ is AbGroup-yielding ) by PRVECT_1:def 10; :: thesis: verum