Clash between KOMA-Script and lmodern: how to fix the \implies bug?

Question

I want to fix the "bug" of the \implies symbol, which is not rendered properly for large font sizes. Accordingly to this answer, I used the lmodern package and redefined a symbol (see the answer).

But there is, seemingly, a clash between KOMA-Script and modern packages, as the MWE shows (the sign \int is not rendered at the right size):

\documentclass{scrreprt}
\usepackage{amsmath}
\usepackage{lmodern}
\KOMAoptions{fontsize=20pt}

\begin{document}

$\displaystyle \int_0^1 f(t) dt \implies 1=1$

\end{document}

So, my question is: How to fix the "bug" of \implies so that it still works with the scrreprt package? The "bug" of \implies is the bumps you can see in the middle of the implies symbol.

---

Remark: I use the KOMA-Script package only to modify the font size in the standalone package, with

\documentclass[class=scrreprt]{standalone}

Answer 1

The fix by egreg in the question you linked too works perfectly also with scrartcl. If you want a larger integral you can load the excale package (after lmodern!):

\documentclass{scrreprt}
\usepackage{amsmath}
\usepackage{lmodern}
\usepackage{exscale}
\KOMAoptions{fontsize=20pt}
\makeatletter
% Load the OT1 definitions for lmodern
\input{ot1lmr.fd}
% Change the definition for \OT1/lmr/m/n/<size>
\DeclareFontShape{OT1}{lmr}{m}{n}%
  {<-5.5>    rm-lmr5  <5.5-6.5> rm-lmr6
   <6.5-7.5> rm-lmr7  <7.5-8.5> rm-lmr8
   <8.5-9.5> rm-lmr9  <9.5->    rm-lmr10
  }{}
\makeatother

\begin{document}

$\displaystyle \int_0^1 f(t) dt \implies 1=1$

\end{document}