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<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#V10" target="_self">Covariant</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="E1:50"/>
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V1" target="_self">Covariant</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D13" target="_self">Def13</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="E3:50"/><i><font color="Green">E37</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> <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#D2" target="_self">Def2</a></i>;<br/>
<i><font color="Green">E38</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"><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#E3:50"><i><font color="Green">E37</font></i></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/>
<i><font color="Green">E39</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"><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#E3:50"><i><font color="Green">E37</font></i></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/>
<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="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>4</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>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="functor0.html#E3:50"><i><font color="Green">E37</font></i></a>, <a class="txt" href="functor0.html#E4:50"><i><font color="Green">E38</font></i></a>, <a class="txt" href="functor0.html#E5:50"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_3.html#T96">FUNCT_3:96</a></i>
;<br/>


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