Cfrgtkky

My proofs often look like this:

documentclass{article}

usepackage{mathtools}

begin{document}

    begin{align}

        &text{First Statement}\

        &implies text{Second Statement}\

        &stackrel{text{Explanation}}{implies}text{Third Statement}\

        &stackrel{mathclap{text{Explanation}}}{implies} text{Fourth Statement}

    end{align}

end{document}

And the issue is that the alignment takes into account the entire stackrel, while I want it to algin with the implication arrow.
I tried stackrel{Explanation}{&implies} but that throws an error.
mathclap works, if the explanation is not too long and doesn't touch the statement after the implication arrow.

Do you have any suggestions how to solve this problem?

The stackrel command is defined as

#1#2 → mathrel{mathop{#2}limits^{#1}}

so you could use smashoperator from the mathtools package to get rid of the space introduced by the left half of the superscript.
I'm defining smashstackrel below, a version of stackrel that incorporates smashoperator. I think smashstackrel[l] does precisely what you want.
I also defined feliximplies{<text>} to make life simpler.

documentclass{article}



usepackage{mathtools}



newcommand*smashstackrel[3][lr]{%

  mathrel{smashoperator[#1]{mathop{#3}^{#2}}}

}



newcommand*feliximplies[1]{smashstackrel[l]{textnormal{#1}}{implies}}



begin{document}



begin{align}

    &text{First Statement}\

    &implies text{Second Statement}\

    &smashstackrel[l]{text{Explanation}}{implies}text{Third Statement}\

    &feliximplies{Explanation} text{Fourth Statement}

end{align}



end{document}

Notes:

• The optional argument of smashstackrel can be either [l], [r] or [lr] depending on whether you want to ignore the left side or the right side or both sides of the superscript for spacing purposes.



• 
  

  implies is defined as DOTSB;Longrightarrow; and ; produces a space that can be stretched (but not shrunk, by default).
  This space will no longer be stretchable if stackrel (or smashstackrel) is used, so doing so feels slightly dubious.
  I think something like

  
  
  

  ;mkern-thickmuskipstackrel{<text>}{implies};mkern-thickmuskip
  
  

  
  
  

  might be more appropriate than just stackrel{<text>}{implies}. This reinserts precisely the amount of stretchability that was lost. (The same remark applies to smashstackrel and noLstackrel, which is defined below.)

  
  
  

  In this case it doesn't matter though, since here the space won't be stretched anyway. It would matter if this command were used inline rather than in a display environment.

  
  
  

  Brief explanation: ; is defined as mskipthickmuskip and inserts a horizontal space of length thickmuskip, which by default is 5mu but can be stretched to 10mu if necessary. mkern is similar to mskip, but it doesn't allow for stretching. So mkern-thickmuskip removes a horizontal space of 5mu in this case so that we end up with a horizontal space of 0mu that can be stretched to up to 5mu. See this answer for more information on spacing commands.

  
  


• 
  

  A possible disadvantage ofsmashstackrel compared to stackrel is that it always typesets things in displaystyle.
  I've included a version of smashstackrel[l] that doesn't do this below because I had already written it before I suddenly remembered the existence of smashoperator.

  
  
  

  makeatletter %% <- make @ usable in command names
  
  newcommand*noLstackrel[2]{mathpalettenoLstackrel@{{#1}{#2}}}
  
  newcommand*noLstackrel@[2]{noLstackrel@@{#1}#2}
  
  newcommand*noLstackrel@@[3]{% #1 = displaystyle etc., #2 = top, #3 = bottom
  
    begingroup                           %% <- limit scope of boxes
  
      sbox0{$m@th#1stackrel{#2}{#3}$}% %% <- put stackrel construction in box 0
  
      sbox2{$m@th#1#3$}%                %% <- put base symbol in box 2
  
      hskip.5wd2 hskip-.5wd0          %% <- remove excess width on the left
  
      mathrel{usebox0}%                 %% <- print box 0
  
    endgroup
  
  }
  
  makeatother  %% <- revert @
  
  

  
  
  

  Usage: noLstackrel{<stuff on top>}{implies}.

  
  

You could try eqnarray

begin{eqnarray}

    && text{First Statement}\

    &implies& text{Second Statement}\

    &stackrel{text{Explanation}}{implies}&text{Third Statement}\

    &stackrel{mathclap{text{Explanation}}}{implies}& text{Fourth Statement}

end{eqnarray}

Reading the documentation on mathtools after learning about smashoperators from Circumscribes answer, I found another possible solution: xRightarrow

documentclass{article}

usepackage{mathtools}

begin{document}

    begin{align}

        &text{Statement}\

        &implies text{implies arrow}\

        &xRightarrow{text{Explanation}}text{xRightarrow}\

        &xRightarrow{(*)} text{xRightarrow}\

        &;xRightarrow{(*)}; text{xRightarrow with ;}\

        &implies text{implies arrow}\

        &;xRightarrow{}; text{xRightarrow with ;}\

        &;Rightarrow; text{Rightarrow with ;}

    end{align}

end{document}

Resulting in:

The advantage of this solution is, that it utilizes a command from a known package, which probably has less errors than a home cooked solution. And it allows for underscript too.
The disadvantage is probably clear from the picture. implies inserts a space before the arrow, which xRightarrow does not do.
(EDIT: this can be fixed with ; at the sides as Circumscribes points out but it is still noticeable that xRightarrow is based on Rightarrow, as you can see from the default length when there is no input)

So instead of implies you would probably have to use Rightarrow instead. Secondly I am not sure if I visually prefer different length arrows over explanations which overflow the width of the usual implies arrow.