reconsider o = ~ the lmult of V as Function of [: the carrier of V, the carrier of (opp K):], the carrier of V ;
let M1, M2 be strict RightModStr over opp K; :: thesis: ( ( for o being Function of [: the carrier of V, the carrier of (opp K):], the carrier of V st o = ~ the lmult of V holds
M1 = RightModStr(# the carrier of V, the addF of V,(0. V),o #) ) & ( for o being Function of [: the carrier of V, the carrier of (opp K):], the carrier of V st o = ~ the lmult of V holds
M2 = RightModStr(# the carrier of V, the addF of V,(0. V),o #) ) implies M1 = M2 )
assume that
A1: for o being Function of [: the carrier of V, the carrier of (opp K):], the carrier of V st o = ~ the lmult of V holds
M1 = RightModStr(# the carrier of V, the addF of V,(0. V),o #) and
A2: for o being Function of [: the carrier of V, the carrier of (opp K):], the carrier of V st o = ~ the lmult of V holds
M2 = RightModStr(# the carrier of V, the addF of V,(0. V),o #) ; :: thesis: M1 = M2
thus M1 = RightModStr(# the carrier of V, the addF of V,(0. V),o #) by A1
.= M2 by A2 ; :: thesis: verum