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<b>let </b><font color="Maroon">c<sub>47</sub></font>, <font color="Maroon">c<sub>48</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">c<sub>49</sub></font>, <font color="Maroon">c<sub>50</sub></font>, <font color="Maroon">c<sub>51</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:37"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="xcmplx_0.html#K4">-</a> 1 &amp; <font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 &amp; <font color="Maroon">c<sub>50</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>48</sub></font> <a href="xcmplx_0.html#K2">+</a> 1 &amp; <font color="Maroon">c<sub>48</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>49</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>47</sub></font> &amp; <font color="Maroon">c<sub>51</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>50</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_1"/>
( <font color="Maroon">c<sub>47</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>47</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> 1 )
 </span><b>by </b><i><a class="txt" href="scpqsort.html#E1:37"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scpqsort.html#E35"><i><font color="Green">Lemma33</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1"><b>suppose </b></a><a NAME="E1:37_1_1"/>
<font color="Maroon">c<sub>47</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:37_1_1"/>
<font color="Maroon">c<sub>51</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:37"><i><font color="Green">E35</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_2"><b>suppose </b></a><a NAME="E1:37_1_2"/>
<font color="Maroon">c<sub>47</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:37_1_2"/>
<font color="Maroon">c<sub>51</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>49</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:37"><i><font color="Green">E35</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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