Definition simpm := (mulm1, mulm0, mul1m, mul0m, mulmA).Canonical andb_monoid := Law andbA andTb andbT.Canonical andb_comoid := ComLaw andbC.Canonical andb_muloid := MulLaw andFb andbF.Canonical orb_monoid := Law orbA orFb orbF.Canonical orb_comoid := ComLaw orbC.Canonical orb_muloid := MulLaw orTb orbT.Canonical addb_monoid := Law addbA addFb addbF.Canonical addb_comoid := ComLaw addbC.Canonical orb_addoid := AddLaw andb_orl andb_orr.Canonical andb_addoid := AddLaw orb_andl orb_andr.Canonical addb_addoid := AddLaw andb_addl andb_addr.Canonical addn_monoid := Law addnA add0n addn0.Canonical addn_comoid := ComLaw addnC.Canonical muln_monoid := Law mulnA mul1n muln1.Canonical muln_comoid := ComLaw mulnC.Canonical muln_muloid := MulLaw mul0n muln0.Canonical addn_addoid := AddLaw mulnDl mulnDr.Canonical maxn_monoid := Law maxnA max0n maxn0.Canonical maxn_comoid := ComLaw maxnC.Canonical maxn_addoid := AddLaw maxn_mull maxn_mulr.Canonical gcdn_monoid := Law gcdnA gcd0n gcdn0.Canonical gcdn_comoid := ComLaw gcdnC.Canonical gcdnDoid := AddLaw muln_gcdl muln_gcdr.Canonical lcmn_monoid := Law lcmnA lcm1n lcmn1.Canonical lcmn_comoid := ComLaw lcmnC.Canonical lcmn_addoid := AddLaw muln_lcml muln_lcmr.Canonical cat_monoid T := Law (@catA T) (@cat0s T) (@cats0 T).Definition bigop := reducebig.

Lemma bigopE : bigop = reducebig.