exp = (-1+[Psi]) [Psi] (-1+[Tau]+[Psi]-2 [Tau] [Psi])^2 (1-2 [Tau])^2+(-1+[Tau]+[Psi]-2 [Tau] [Psi])^2 (-1+[Tau]+[Psi])^2 (1-[Psi]+[Tau] (-1+2 [Psi]))-([Tau]-[Psi])^2 ([Tau]+[Psi]-2 [Tau] [Psi]) (2+[Tau]^2 (1-2 [Psi])^2+(-4+[Psi]) [Psi]-2 [Tau] (-2+[Psi]) (-1+2 [Psi]))

Simplify[exp>0,1>[Tau]>1/2&&1>[Psi]>1/2&&vh>vl>0&&[Gamma]>0&&[Tau]<[Psi]]
True