for R being Ring
for P being Ideal of R
for M being Submodule of P
for a being BinOp of P
for z being Element of P
for m being Function of [:P, the carrier of R:],P st a = the addF of R | [:P,P:] & m = the multF of R | [:P, the carrier of R:] & z = the ZeroF of R holds
RightModStr(# the carrier of M, the addF of M, the ZeroF of M, the rmult of M #) = RightModStr(# P,a,z,m #)