How to adjust the sign of implication sign

Question

I want to get the following implication arrows:

But according to percusse's suggestion not implies, not Leftarrow, description in the middle of an arrow in TikZ-cd I would get this:

As you can see, I want to get the implication sign with large distance between two parallel curves, not the large width of each of the two curves. Can tikz-cd do this?

Here is the modification of percusse's tex file:

\documentclass{article}
\usepackage{tikz-cd}
\usetikzlibrary{decorations.markings}
\tikzset{degil/.style={line width=1.5pt,
        decoration={markings,
        mark= at position 0.5 with {
              \node[transform shape] (tempnode) {$\backslash\backslash$};
              %\draw[thick] (tempnode.north east) -- (tempnode.south west);
              }
          },
          postaction={decorate}
}
}

\tikzset{
commutative diagrams/.cd,
arrow style=tikz,
diagrams={>=open triangle 45, line width=1.5pt}}


\begin{document}

\begin{tikzcd}[arrows=Rightarrow]
\fbox{\parbox{2cm}{$f$ is differentiable at point $P$}}
\arrow[bend right]{rr}{} &\quad    
\qquad&\fbox{\parbox{2cm}{$f$ is continuous at $P$}}\arrow[bend right,degil]{ll}{}
\end{tikzcd}
\end{document}

Answer 1

The double distance key is useful here (see the TikZ manual, p161).

\documentclass{article}
\usepackage{tikz-cd}
\usetikzlibrary{arrows}
\usetikzlibrary{decorations.markings}
\tikzset{degil/.style={line width=0.5pt,double distance=5pt,
        decoration={markings,
        mark= at position 0.5 with {
              \node[transform shape] (tempnode) {$\backslash\backslash$};
              %\draw[thick] (tempnode.north east) -- (tempnode.south west);
              }
          },
          postaction={decorate}
}
}

\tikzset{
commutative diagrams/.cd,
arrow style=tikz,
diagrams={>=open triangle 45, line width=0.5pt}}


\begin{document}

\begin{tikzcd}[arrows=Rightarrow]
\fbox{\parbox{2cm}{$f$ is differentiable at point $P$}}
\arrow[bend right,double distance=5pt]{rr}{} &\quad    
\qquad&\fbox{\parbox{2cm}{$f$ is continuous at $P$}}\arrow[bend right,degil]{ll}{}
\end{tikzcd}
\end{document}