... IndFD(Wδ)=MF, then MF⊕ IndFD(Wδ)isan(F,δ)-framed VOA. Beforewe prove Theorem 3.21, we note that the conditions of Theorem 3.21 including the fusion rule (3.21) follow from the conditions of Theorem ... ∈Iα}Annals of Mathematics, 159 (2004), 535–596A new construction of the moonshinevertex operator algebra over the real number fieldBy Masahiko Miyamoto*AbstractWe give a new construction of the moonshine ... 3.20.Proposition 3.22. Assume the triple (D, α, β) satisfies the conditions of Theorem 3.20 for any α, β ∈δ, γ. Then IndFD(Wα)×IndFD(Wβ)= IndFD(Wα+β)for α, β ∈δ, γ.Proof of Theorem 3.21....