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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="cat_3.html#K2" target="_self">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>assume </b><a NAME="E1:57"/><i><font color="Green">E33</font></i>: 
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:57_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><b>hence </b><span class="p1">(<span class="default"><a href="cat_3.html#K3" target="_self">doms</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cat_3.html#K2" target="_self">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cat_3.html#K2" target="_self">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="cat_3.html#D3" target="_self">Def3</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="cat_3.html#E1:57"><i><font color="Green">E33</font></i></a>, <a class="txt" href="cat_3.html#E1:57_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="cat_3.html#T2" target="_self">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cat_3.html#K2" target="_self">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="cat_3.html#E1:57_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="cat_3.html#T2" target="_self">Th2</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b> <a href="cat_3.html#K3" target="_self">doms</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cat_3.html#K2" target="_self">.--&gt;</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<font color="Maroon">c<sub>1</sub></font> <a href="cat_3.html#K2" target="_self">.--&gt;</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="cat_3.html#T1" target="_self">Th1</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> <a href="cat_3.html#K1" target="_self">--&gt;</a> <font color="Maroon">c<sub>3</sub></font>

;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="cat_3.html#D14" target="_self">CAT_3:def 14</a><br/>


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