math mode align expressions too far apart

Question

I am attempting to allow following expressions in math mode:

\begin{flalign*}
  \Gamma_1 ; x : T ; \Gamma_2 \vdash{}& x
  &&\Rightarrow T & \\
  \Gamma \vdash&{} \lambda(z : T).t
  &&\Rightarrow \forall(z : T) U, & \\
\end{flalign*}

It produces text similar to following:

Γ 1 ; x ∶ T ; Γ 2 ⊢ x                   ⇒ T
                Γ ⊢λ(z ∶ T ).t          ⇒ ∀(z ∶ T )U,

My problem with it, is the \Rightarrow is too far apart from whatever expression that comes after \vdash immediately.

I wish I can produce following results as alignment:

Γ 1 ; x ∶ T ; Γ 2 ⊢ x           ⇒ T
                Γ ⊢ λ(z ∶ T ).t ⇒ ∀(z ∶ T )U,

Note that, the \Rightarrow only goes as far as it needed, not far apart to form a separate column. Searching around the internet, there are examples aligning pushing to left by adding a trailing &, but for some reason it does not work in my case. How would you solve this problem?

Answer 1

Like this? I took the liberty to replace the . (in the second line) with a \cdot which I thought more appropriate:

\documentclass{article}

\usepackage{mathtools, nccmath}

\begin{document}

Some text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text. Some more text.
\begin{fleqn}[\parindent]
\begin{alignat*}{2}
    \Gamma_1 ; x : T ; \Gamma_2 & \vdash{} x
  &&\Rightarrow T \\
  \Gamma & \vdash \lambda(z : T)\cdot t
  &&\Rightarrow \forall(z : T) U,
   \end{alignat*}
\end{fleqn}

\end{document}