let G be Group; :: thesis: for H being Subgroup of G st the carrier of G c= the carrier of H holds
multMagma(# the carrier of H,the multF of H #) = multMagma(# the carrier of G,the multF of G #)
let H be Subgroup of G; :: thesis: ( the carrier of G c= the carrier of H implies multMagma(# the carrier of H,the multF of H #) = multMagma(# the carrier of G,the multF of G #) )
A1: the carrier of H c= the carrier of G by Def5;
assume the carrier of G c= the carrier of H ; :: thesis: multMagma(# the carrier of H,the multF of H #) = multMagma(# the carrier of G,the multF of G #)
then A2: the carrier of G = the carrier of H by A1, XBOOLE_0:def 10;
G is Subgroup of G by Th63;
hence multMagma(# the carrier of H,the multF of H #) = multMagma(# the carrier of G,the multF of G #) by A2, Th68; :: thesis: verum