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<span class="kw">let </span><font color="Maroon" title="c1">B</font>, <font color="Maroon" title="c2">A</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">B</font><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/> for <font color="Olive" title="b4">f</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c1">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/> for <font color="Olive" title="b3">f</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Olive" title="b1">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  for <font color="Olive" title="b1">f</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c4">a</font></span>)</span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:31"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c4">a</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">f</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c4">a</font></span>)</span></span><br/>

<a NAME="E2:31"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c4">a</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T27" title="CAT_1:th.27">CAT_1:27</a></span>;<br/>
<a NAME="E3:31"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c5">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T27" title="CAT_1:th.27">CAT_1:27</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T20" target="_self" title="NATTRA_1:th.20">Th21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T15" target="_self" title="NATTRA_1:th.15">Th15</a></span>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c6">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="#E3:31"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="nattra_1.html#T13" target="_self" title="NATTRA_1:th.13">Th13</a></span>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="cat_1.html#T28" title="CAT_1:th.28">CAT_1:28</a></span>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="cat_1.html#T29" title="CAT_1:th.29">CAT_1:29</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="nattra_1.html#T13" target="_self" title="NATTRA_1:th.13">Th13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c4">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T15" target="_self" title="NATTRA_1:th.15">Th15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" title="NATTRA_1:func.4">id</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c4">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T20" target="_self" title="NATTRA_1:th.20">Th21</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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