for M being non empty multLoopStr
for H1, H2 being non empty MonoidalSubStr of M st the carrier of H1 = the carrier of H2 holds
multLoopStr(# the carrier of H1, the multF of H1, the OneF of H1 #) = multLoopStr(# the carrier of H2, the multF of H2, the OneF of H2 #)