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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:5"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E2:5"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E3:5"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:5"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E5:5"/><i><font color="Green">E10</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E6:5"/><i><font color="Green">E11</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<a NAME="E7:5"/><i><font color="Green">E12</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E8:5"/><i><font color="Green">E13</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<i><font color="Green">E14</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="scmbsort.html#E7:5"><i><font color="Green">E12</font></i></a>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="scmbsort.html#E8:5"><i><font color="Green">E13</font></i></a>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:5"><i><font color="Green">E9</font></i></a>, <a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E3:5"><i><font color="Green">E8</font></i></a>, <a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
;<br/>
<a NAME="E10:5"/><i><font color="Green">E15</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>
<a NAME="E11:5"/><i><font color="Green">E16</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E12:5"/>
 <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="funct_1.html#T52">FUNCT_1:52</a></i>;<br/>
<b>then </b><i><font color="Green">E17</font></i>:  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T55">FUNCT_1:55</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E10:5"><i><font color="Green">E15</font></i></a>, <a class="ref" href="funct_1.html#T67">FUNCT_1:67</a></i>
;<br/>
<a NAME="E14:5"/><b>then </b>
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E3:5"><i><font color="Green">E8</font></i></a>, <a class="txt" href="scmbsort.html#E11:5"><i><font color="Green">E16</font></i></a>, <a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>;<br/>
<a NAME="E15:5"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T18">FUNCT_4:18</a></i>;<br/>
<a NAME="E16:5"/><b>then </b><i><font color="Green">E18</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/>
<a NAME="E17:5"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T18">FUNCT_4:18</a></i>;<br/>
<a NAME="E18:5"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E16:5"><i><font color="Green">E18</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E19:5"/><i><font color="Green">E20</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E20:5"/><b>then </b><i><font color="Green">E21</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E4:5"><i><font color="Green">E9</font></i></a>, <a class="txt" href="scmbsort.html#E9:5"><i><font color="Green">E14</font></i></a>, <a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>;<br/>
<a NAME="E21:5"/><i><font color="Green">E22</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E4:5"><i><font color="Green">E9</font></i></a>, <a class="txt" href="scmbsort.html#E9:5"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scmbsort.html#E18:5"><i><font color="Green">E19</font></i></a>, <a class="txt" href="scmbsort.html#E19:5"><i><font color="Green">E20</font></i></a>, <a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>;<br/>
<a NAME="E22:5"/><i><font color="Green">E23</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E9:5"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scmbsort.html#E18:5"><i><font color="Green">E19</font></i></a>, <a class="txt" href="scmbsort.html#E20:5"><i><font color="Green">E21</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>
<div><i><font color="Green">E24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="5_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:5_3"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:5_3"/><b>then </b><i><font color="Green">E26</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E9:5"><i><font color="Green">E14</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:5_3_1"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_3_1_1"><b>suppose </b></a><a NAME="E1:5_3_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E2:5_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a></i>
<br/>.= 
<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:5_3_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scmbsort.html#T5" target="_self">Th5</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_3_1_2"><b>suppose </b></a><a NAME="E1:5_3_1_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_3_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_3_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:5_3_1_2_1_1"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_3_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:5_3_1_2_1_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E2:5_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="scmbsort.html#T5" target="_self">Th5</a></i>
<br/>.= 
<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:5_3_1_2_1_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_3_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:5_3_1_2_1_1_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E2:5_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmbsort.html#E1:5_3_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scmbsort.html#T6" target="_self">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:5_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:5_3_1_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmbsort.html#E1:5_3_1_2_1_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmbsort.html#T6" target="_self">Th6</a></i>
<br/>.= 
<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:5_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:5_3_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E24:5"/><b>then </b><i><font color="Green">E25</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E22:5"><i><font color="Green">E23</font></i></a>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>
<a NAME="E25:5"/><i><font color="Green">E26</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E13:5"><i><font color="Green">E17</font></i></a>, <a class="txt" href="scmbsort.html#E22:5"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scmbsort.html#E23:5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>
<a NAME="E26:5"/><i><font color="Green">E27</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E9:5"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scmbsort.html#E24:5"><i><font color="Green">E25</font></i></a>, <a class="ref" href="funct_1.html#T53">FUNCT_1:53</a></i>;<br/>
<a NAME="E27:5"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T25">FUNCT_1:25</a></i>;<br/>
<a NAME="E28:5"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E29:5"/><b>then </b><i><font color="Green">E28</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E5:5"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scmbsort.html#E9:5"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scmbsort.html#E21:5"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmbsort.html#E25:5"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E30:5"/><i><font color="Green">E29</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E5:5"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scmbsort.html#E9:5"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scmbsort.html#E21:5"><i><font color="Green">E22</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:5_4"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:5_4"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E30:5"><i><font color="Green">E29</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:5_4_1"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_4_1_1"><b>suppose </b></a><a NAME="E1:5_4_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:5_4_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E1:5"><i><font color="Green">E6</font></i></a>, <a class="txt" href="scmbsort.html#E2:5_4"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmbsort.html#T4" target="_self">Th4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_4_1_2"><b>suppose </b></a><a NAME="E1:5_4_1_2"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_4_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_4_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:5_4_1_2_1_1"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_4_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:5_4_1_2_1_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:5_4_1_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmbsort.html#E2:5"><i><font color="Green">E7</font></i></a>, <a class="txt" href="scmbsort.html#E2:5_4"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmbsort.html#T5" target="_self">Th5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_4_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:5_4_1_2_1_1_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E2:5_4"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmbsort.html#E1:5_4_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmbsort.html#T6" target="_self">Th6</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:5_4"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="scmbsort.html#E6:5"><i><font color="Green">E11</font></i></a>, <a class="txt" href="scmbsort.html#E1:5_4"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmbsort.html#E1:5_4_1_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmbsort.html#E1:5_4_1_2_1_1_2"><i><font color="Green">E33</font></i></a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:5_4_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p5">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E32:5"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E30:5"><i><font color="Green">E29</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>
<b>hence </b><a NAME="E33:5"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scmbsort.html#E9:5"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scmbsort.html#E26:5"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmbsort.html#E29:5"><i><font color="Green">E28</font></i></a>, <a class="ref" href="rfinseq.html#T3">RFINSEQ:3</a></i>;<br/>


</div>
