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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">A</font> is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a>  &amp; <font color="Maroon" title="c2">B</font> is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a>  implies <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a>  )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:76"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
<font color="Maroon" title="c1">A</font> is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a> 
 <span class="kw">and </span><br/><a NAME="E2:76"/><span class="lab"><font color="Green" title="E55">A2</font></span>: 
<font color="Maroon" title="c2">B</font> is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> is  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">NATTRA_1:def 19</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> st <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c4">f1</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c5">f2</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E4:76"/><span class="lab"><font color="Green" title="E56">A3</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c4">f1</font>,<font color="Maroon" title="c5">f2</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="domain_1.html#T9" title="DOMAIN_1:th.9">DOMAIN_1:9</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E6:76"/><span class="lab"><font color="Green" title="E57">A4</font></span>: 
<font color="Maroon" title="c5">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c6">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def19</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font><span class="kw"> such that </span><br/><a NAME="E8:76"/><span class="lab"><font color="Green" title="E58">A5</font></span>: 
<font color="Maroon" title="c4">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def19</a></span>;<br/>
<span class="kw">take </span>
<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span><br/>

<span class="kw">thus </span><a NAME="E9:76"/>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:76"><span class="lab"><font color="Green" title="E56">A3</font></span></a>, <a class="txt" href="#E8:76"><span class="lab"><font color="Green" title="E58">A5</font></span></a>, <a class="txt" href="#E6:76"><span class="lab"><font color="Green" title="E57">A4</font></span></a>, <a class="ref" href="cat_2.html#T41" title="CAT_2:th.41">CAT_2:41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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