# Question about Ext group in $\mathcal{O}^\mathfrak{p}$?

Let $$W$$ be a Weyl group, let $$\mu$$ be an antidominant weight. Let $$W_I$$ be the Weyl group generated by $$I$$ and $$w_I$$ be the longest element in $$W_I$$. Denote $${}^IW$$ the set of minimal length coset representative of $$W_I\backslash W$$.

Given $$w_Iw\le w_Iw'$$, $$x,w,w'\in {}^IW$$, does it implies $$\dim \text{Ext}^i_{\mathcal{O}^\mathfrak{p}}(M_I(w_Ix\cdot \mu),L(w_Iw\cdot \mu))\le \dim \text{Ext}^i_{\mathcal{O}^\mathfrak{p}}(M_I(w_Ix\cdot \mu),L(w_Iw'\cdot \mu))$$?