<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="altcat_1.html#L1">AltGraph</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="functor0.html#V11" target="_self">Contravariant</a>  <a href="functor0.html#L2" target="_self">FunctorStr</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:52"/>
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V2" target="_self">Contravariant</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D14" target="_self">Def14</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E3:52"/><i><font color="Green">E39</font></i>: 
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a>  <a href="functor0.html#K1" target="_self">~</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K16">:]</a></span>
 <b>by </b><i><a class="ref" href="functor0.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E4:52"/><i><font color="Green">E40</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K16">:]</a></span> <a href="hidden.html#R1">=</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>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:52"/><b>then </b><i><font color="Green">E41</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K16">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<i><font color="Green">E42</font></i>: <font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default">the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> 

<br/>.= 
<span class="p1">(<span class="default">the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K1">`1</a> 

<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K16">:]</a></span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="txt" href="functor0.html#E3:52"><i><font color="Green">E39</font></i></a>, <a class="txt" href="functor0.html#E5:52"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_4.html#D2">FUNCT_4:def 2</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="ref" href="funct_3.html#T96">FUNCT_3:96</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
;<br/>
<a NAME="E7:52"/><i><font color="Green">E43</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K16">:]</a></span>
 
<b>by </b><i><a class="txt" href="functor0.html#E4:52"><i><font color="Green">E40</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<i><font color="Green">E44</font></i>: <font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default">the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> 

<br/>.= 
<span class="p1">(<span class="default">the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K1">`1</a> 

<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K16">:]</a></span> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span></span>)</span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="txt" href="functor0.html#E3:52"><i><font color="Green">E39</font></i></a>, <a class="txt" href="functor0.html#E7:52"><i><font color="Green">E43</font></i></a>, <a class="ref" href="funct_4.html#D2">FUNCT_4:def 2</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="ref" href="funct_3.html#T96">FUNCT_3:96</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
;<br/>
<a NAME="E9:52"/><i><font color="Green">E45</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K16">:]</a></span>
 
<b>by </b><i><a class="txt" href="functor0.html#E4:52"><i><font color="Green">E40</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>thus </b>the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> = 
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
<span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="funct_3.html#K16">:]</a></span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="functor0.html#E3:52"><i><font color="Green">E39</font></i></a>, <a class="txt" href="functor0.html#E9:52"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_4.html#D2">FUNCT_4:def 2</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="functor0.html#E6:52"><i><font color="Green">E42</font></i></a>, <a class="txt" href="functor0.html#E8:52"><i><font color="Green">E44</font></i></a>, <a class="ref" href="funct_3.html#T96">FUNCT_3:96</a></i>
;<br/>


</div>
