deletions | additions       diff --git a/Ex 1.tex b/Ex 1.tex  index 63271de..93d34cd 100644  --- a/Ex 1.tex  +++ b/Ex 1.tex 
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\newcommand{\if}[2]{if(#1) \ \{ #2 \}}  \newcommand{\else}[1]{else \ \{ #1 \}}  \newcommand{\ie}[3]{\if{#1}{#2} \ \else{#3}}  \newcommand{\a}[0]{\land}  Given:  \begin{equation}  \begin{split}  Q &= \empty\\  R &= 0 \leq y \land \a  (0 \leq x \to y = x) \land \a  (x < 0 \to y = -x) \end{split}  \end{equation}  \begin{equation}  \begin{split}  & \wp{\ie{x < 0}{y := -x}{ y := x }}{R} \\  \iff & (x < 0 \to \wp{y:= -x}{R}) \land \a  (0 \leq x \to \wp{y:= x}{R})\\ \iff & (x < 0 \to (0 \leq -x \land \a  (0 \leq x \to -x = x) \land \a  (x < 0 \to -x = -x )))\\ \land & (x \leq 0 \to (0 \leq x \land \a  (0 \leq x \to x = x) \land \a  (x < 0 \to x = -x))) -x)))\\  \iff & (x < 0 \to -x = -x) \a (0 \leq x \to x = x)\\  \iff & T  \end{split}  \end{equation}