let G be finite Group; :: thesis: for H being Subgroup of G st card G = card 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: ( card G = card H implies multMagma(# the carrier of H, the multF of H #) = multMagma(# the carrier of G, the multF of G #) )
assume A1: card G = card H ; :: thesis: multMagma(# the carrier of H, the multF of H #) = multMagma(# the carrier of G, the multF of G #)
A2: the carrier of H c= the carrier of G by Def5;
the carrier of H = the carrier of G

proof

assume the carrier of H <> the carrier of G ; :: thesis: contradiction
then the carrier of H c< the carrier of G by A2;
hence contradiction by A1, CARD_2:48; :: thesis: verum

end;

hence multMagma(# the carrier of H, the multF of H #) = multMagma(# the carrier of G, the multF of G #) by Th61; :: thesis: verum