Let $(X,\mathcal U)$ be a uniform space and let $U\in \mathcal U$. Is this statement true? $$\forall V\in \mathcal U, \exists W\in \mathcal U, V\circ U\subseteq U\circ W$$

I think if the above statement is true then we can easily prove: $$\forall V\in \mathcal U, \exists W\in \mathcal U, U\circ V\subseteq W\circ U$$

Let $(X,\mathcal U)$ be a uniform space and let $U\in \mathcal U$. Is this statement true? $$\forall V\in \mathcal U, \exists W\in \mathcal U, U\circ W\subseteq V\circ U$$

I think if the above statement is true then we can easily prove: $$\forall V\in \mathcal U, \exists W\in \mathcal U, W\circ U\subseteq U\circ V$$

Let $(X,\mathcal U)$ be a uniform space and let $U\in \mathcal U$. Is this statement true: $$\forall V\in \mathcal U, \exists W\in \mathcal U, V\circ U\subseteq U\circ W$$

Let $(X,\mathcal U)$ be a uniform space and let $U\in \mathcal U$. Is this statement true? $$\forall V\in \mathcal U, \exists W\in \mathcal U, V\circ U\subseteq U\circ W$$

I think if the above statement is true then we can easily prove: $$\forall V\in \mathcal U, \exists W\in \mathcal U, U\circ V\subseteq W\circ U$$

Let $(X,\mathcal U)$ be a uniform space and let $U\in \mathcal U$. Is this statement true: $$\forall V\in \mathcal U, \exists W\in \mathcal U, V\circ U=U\circ W$$

Let $(X,\mathcal U)$ be a uniform space and let $U\in \mathcal U$. Is this statement true: $$\forall V\in \mathcal U, \exists W\in \mathcal U, V\circ U\subseteq U\circ W$$