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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V2">transitive</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V2">transitive</a>  <a href="altcat_2.html#M1" target="_self">SubCatStr</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:55"/><i><font color="Green">E26</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:55"/><i><font color="Green">E27</font></i>: 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>2</sub></font> <a href="altcat_2.html#R2" target="_self">cc=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>thus </b><a NAME="E3:55"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="altcat_2.html#E1:55"><i><font color="Green">E26</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D11" target="_self">ALTCAT_2:def 11</a><br/>

<b>thus </b><a NAME="E4:55"/>
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>2</sub></font> <a href="altcat_2.html#R2" target="_self">cc=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="altcat_2.html#E2:55"><i><font color="Green">E27</font></i></a></i>;<br/>

<b>thus </b><a NAME="E5:55"/>
<span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K3">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span><a href="zfmisc_1.html#K3">:]</a></span>
 <b>by </b><i><a class="txt" href="altcat_2.html#E1:55"><i><font color="Green">E26</font></i></a>, <a class="ref" href="mcart_1.html#T77">MCART_1:77</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D2" target="_self">ALTCAT_2:def 2</a><br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E6:55"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K3">:]</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:55"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 <b>and </b><br/><a NAME="E9:55"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K3">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="mcart_1.html#K3">]</a></span>
 <b>by </b><i><a class="ref" href="mcart_1.html#T72">MCART_1:72</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>7</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="altcat_2.html#E8:55"><i><font color="Green">E29</font></i></a></i>;<br/>
<a NAME="E11:55"/>
(  not <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="altcat_1.html#D4">ALTCAT_1:def 4</a></i>;<br/>
<a NAME="E12:55"/><b>then </b><i><font color="Green">E31</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T113">ZFMISC_1:113</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="altcat_1.html#K4">.</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> ;<br/>
<a NAME="E14:55"/><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="altcat_2.html#E12:55"><i><font color="Green">E31</font></i></a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="altcat_2.html#E1:55"><i><font color="Green">E26</font></i></a>, <a class="txt" href="altcat_2.html#E8:55"><i><font color="Green">E29</font></i></a></i>;<br/>
<a NAME="E16:55"/>
(  not <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="altcat_1.html#D4">ALTCAT_1:def 4</a></i>;<br/>
<a NAME="E17:55"/><b>then </b><i><font color="Green">E33</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T113">ZFMISC_1:113</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>3</sub></font> <a href="altcat_1.html#K4">.</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> ;<br/>
<a NAME="E19:55"/>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E20:55"/><b>then </b><i><font color="Green">E34</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="altcat_2.html#E2:55"><i><font color="Green">E27</font></i></a>, <a class="ref" href="altcat_2.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E21:55"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="altcat_2.html#E17:55"><i><font color="Green">E33</font></i></a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E22:55"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>11</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="altcat_2.html#E14:55"><i><font color="Green">E32</font></i></a>, <a class="txt" href="altcat_2.html#E20:55"><i><font color="Green">E34</font></i></a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<div><i><font color="Green">E36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>16</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:55_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="altcat_2.html#D11" target="_self">Def11</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="altcat_2.html#E8:55"><i><font color="Green">E29</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>20</sub></font> = the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>1</sub></font> <a href="altcat_1.html#K4">.</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>,<span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> ;<br/><a NAME="E4:55_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="domain_1.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="multop_1.html#D1">MULTOP_1:def 1</a></i>;<br/><a NAME="E5:55_1"/><i><font color="Green">E38</font></i>: 
<span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span><a href="zfmisc_1.html#K3">:]</a></span>
 <b>by </b><i><a class="txt" href="altcat_2.html#E1:55"><i><font color="Green">E26</font></i></a>, <a class="txt" href="altcat_2.html#E8:55"><i><font color="Green">E29</font></i></a>, <a class="ref" href="mcart_1.html#T73">MCART_1:73</a></i>;<br/><b>assume </b><a NAME="E6:55_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E7:55_1"/><i><font color="Green">E40</font></i>: 
the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>3</sub></font> <a href="altcat_2.html#R2" target="_self">cc=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="altcat_2.html#D11" target="_self">Def11</a></i>;<br/><a NAME="E8:55_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="domain_1.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="multop_1.html#D1">MULTOP_1:def 1</a></i>;<br/><a NAME="E9:55_1"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="altcat_2.html#E4:55_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="altcat_2.html#E5:55_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="altcat_2.html#E7:55_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="altcat_2.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E10:55_1"/><i><font color="Green">E42</font></i>: 
the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="altcat_2.html#R2" target="_self">cc=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="altcat_2.html#D11" target="_self">Def11</a></i>;<br/><a NAME="E11:55_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="domain_1.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="multop_1.html#D1">MULTOP_1:def 1</a></i>;<br/><a NAME="E12:55_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="txt" href="altcat_2.html#E6:55"><i><font color="Green">E28</font></i></a>, <a class="txt" href="altcat_2.html#E9:55"><i><font color="Green">E30</font></i></a>, <a class="txt" href="altcat_2.html#E4:55_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="altcat_2.html#E10:55_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="altcat_2.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font> = 
<font color="Maroon">c<sub>20</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="txt" href="altcat_2.html#E6:55_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="txt" href="altcat_2.html#E22:55"><i><font color="Green">E35</font></i></a>, <a class="txt" href="altcat_2.html#E6:55_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="altcat_2.html#E9:55_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E24:55"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="altcat_2.html#E9:55"><i><font color="Green">E30</font></i></a>, <a class="ref" href="multop_1.html#D1">MULTOP_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E25:55"/>
the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="altcat_2.html#E22:55"><i><font color="Green">E35</font></i></a>, <a class="txt" href="altcat_2.html#E23:55"><i><font color="Green">E36</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>


</div>
