 For a (∨,0)-semilattice, the larger semilattice "R(S)" is the (∨,0)-semilattice freely generated by new elements "t(a,b,c)", for "a, b, c" in "S" such that "c ≤ a ∨ b", subjected to the only relations "c=t(a,b,c) ∨ t(b,a,c)" and "t(a,b,c) ≤ a".Iterating this construction gives the "free distributive extension" formula_11 of "S".Now, for a set Ω, let "L(Ω)" be the (∨,0)-semilattice defined by generators 1 and "ai,x", for "i<2" and "x" in Ω, and relations "a0,x ∨ a1,x=1", for any "x" in Ω.