let G1, G2, G3 be non empty associative multMagma ; :: thesis: <*G1,G2,G3*> is associative HGrStr-Family of {1,2,3}
reconsider A = <*G1,G2,G3*> as HGrStr-Family of {1,2,3} ;
A is associative

proof

let x be Element of {1,2,3}; :: according to GROUP_7:def 7 :: thesis: A . x is associative
( x = 1 or x = 2 or x = 3 ) by ENUMSET1:def 1;
hence A . x is associative by FINSEQ_1:62; :: thesis: verum

end;

hence <*G1,G2,G3*> is associative HGrStr-Family of {1,2,3} ; :: thesis: verum