I have the following:

$Assumptions = {0 < Ijm1 < Ij < Ijp1 < 1, bpjm1 < 0, bpj < 0, 
bpjp1 < 0, Ijm1 \[Element] Reals, Ij \[Element] Reals, 
Ijp1 \[Element] Reals, bpjm1 \[Element] Reals, bjp \[Element] Reals,
bpjp1 \[Element] Reals};

x = (1 - bpjp1 Ijp1 + bpjp1 Ijp1^2) ;
y = bpj (Ij - Ijm1) (-1 + Ij (1 + bpjp1 (-1 + Ijp1)) - 
bpjp1 (-1 + Ijp1) Ijp1)

When checking inequalities I get

In[243]:= Simplify[x > 0]
Out[243]= True

In[244]:= Simplify[y > 0]
Out[244]= True

but

In[245]:= Simplify[x + y > 0]  
Out[245]= 
1 + bpjp1 (-1 + Ijp1) Ijp1 + 
bpj (Ij - Ijm1) (-1 + Ij (1 + bpjp1 (-1 + Ijp1)) - 
bpjp1 (-1 + Ijp1) Ijp1) > 0

Why?