如何对齐文本和数组？

Question

所以我希望有一些左对齐的文本和它旁边的数组。但是，当我尝试时，数组略高于文本（下面添加的图片）。即使\aligned不起作用。如果这与问题相关，文本位于证明环境中。我已经包含了证明环境

\declaretheoremstyle[
spaceabove=0pt, 
spacebelow=1pt,
headfont=\it,
bodyfont=\normalfont,
postheadspace=6pt,
qed=\qedsymbol,
headpunct=
]{mypf}
\declaretheorem[numbered=no, name=Proof, style=mypf]{pf}

\begin{pf}    
\textbf{N2} (\textit{Positive homogeneity}) $||\lambda v||=d(\lambda v,\lambda 0)=|\lambda | d(v,0)=|\lambda | \cdot||v||.$  \vspace{0.1cm} \\
        $\begin{aligned}
        \left.\textbf{N3 }  (\textit{Triangle inequality})
        \right. \begin{array}{lll}
               ||v+w||=d(v+w,0)&\leq &d(v+w,w) + d(w,0)  \\
              &=& ||v||+||w||
        \end{array}
        \end{aligned}
        \end{pf}

Answer 1

我不会array在aligned环境中嵌套环境。使用单个aligned环境就足够了。

对于下面的截图，我还用 替换了所有 的实例|...|，并用 替换\abs{...}了所有 的实例，其中和是借助包的指令定义的宏。还请注意环境定位说明符的使用，它允许将 QED 符号放在底行。最后，我创建了一个名为 的宏来指示“距离指示器”；采用这种方式可以改善和之间的间距。|| ... ||\norm{...}\abs\norm\DeclarePairedDelimitermathtools[b]aligned\dist\abs{\lambda}d(v,0)

\documentclass{article}
\usepackage{mathtools} 
\DeclareMathOperator{\dist}{\mathit{d}}
\DeclarePairedDelimiter\abs\lvert\rvert
\DeclarePairedDelimiter\norm\lVert\rVert

\usepackage{amsthm,thmtools}
\declaretheoremstyle[
    spaceabove=0pt, 
    spacebelow=1pt,
    headfont=\it,
    bodyfont=\normalfont,
    postheadspace=6pt,
    qed=\qedsymbol,
    headpunct=
]{mypf}
\declaretheorem[numbered=no, name=Proof, style=mypf]{pf}

\begin{document}

\begin{pf}    
\textbf{N2} (\textit{Positive homogeneity}) 
$\norm{\lambda v}=\dist(\lambda v,\lambda 0)
      = \abs{\lambda} \dist(v,0)     
      = \abs{\lambda}\cdot\norm{v}.$   

\medskip\noindent
\hspace{3.15em}%
$\begin{aligned}[b]
\text{\textbf{N3} (\textit{Triangle inequality}) }
     \norm{v+w}&=    \dist(v+w,0) \\
               &\leq \dist(v+w,w) + \dist(w,0) \\
               &=    \norm{v}+\norm{w}\,.
\end{aligned}$
\end{pf}
\end{document}

Answer 2

我建议使用这种变体布局，基于alignedat{3}两条线路的单一布局。它使用 \mathrlap来自的命令mathtools：

\documentclass{article}
\usepackage{mathtools, amssymb}
\usepackage{amsthm, thmtools}

\declaretheoremstyle[
spaceabove=0pt,
spacebelow=1pt,
headfont=\itshape,
bodyfont=\normalfont,
postheadspace=6pt,
qed=\qedsymbol,
headpunct=
]{mypf}

\declaretheorem[numbered=no, name=Proof, style=mypf]{pf}

\begin{document}

\begin{pf}\!: \\[1ex]
$ \begin{alignedat}[b]{3}
& \textbf{N2}\ (\textit{Positive homogeneity})& \|\lambda v\|&=d(\lambda v,\lambda 0)\mathrlap{=|\lambda| d(v,0)=|\lambda | \cdot\|v\|. }\\[1ex]
& \textbf{N3 }(\textit{Triangle inequality}) & \|v+w\| & =d(v+w,0) & & \leq d(v+w,w) + \mathrlap{d(w,0)} \\
 & & & & & = \|v\|+\|w\|
\end{alignedat} $
 \end{pf}

\end{document}