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<b>let </b><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">T</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">D</font><br/> for <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">c'</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>  st  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Olive" title="b2">c</font>,<font color="Olive" title="b3">c'</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">c</font>,<font color="Olive" title="b3">c'</font> holds  <font color="Olive" title="b1">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Olive" title="b2">c</font>,<font color="Olive" title="b1">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Olive" title="b3">c'</font></span><br/><b>let </b><font color="Maroon" title="c3">T</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">c</font>, <font color="Olive" title="b2">c'</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>  st  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Olive" title="b1">c</font>,<font color="Olive" title="b2">c'</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">c</font>,<font color="Olive" title="b2">c'</font> holds  <font color="Maroon" title="c3">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Olive" title="b1">c</font>,<font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Olive" title="b2">c'</font></span><br/><b>let </b><font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">c'</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">c'</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">c</font>,<font color="Maroon" title="c5">c'</font> holds  <font color="Maroon" title="c3">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c5">c'</font> )</span><br/>







<b>assume </b><a NAME="E1:105"/><i><font color="Green" title="E59">A1</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">c'</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:()"><i><font color="Red">::  thesis: </font></i></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">c</font>,<font color="Maroon" title="c5">c'</font> holds  <font color="Maroon" title="c3">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c5">c'</font></span><br/>

<b>let </b><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">c</font>,<font color="Maroon" title="c5">c'</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c5">c'</font></span><br/>

<a NAME="E2:105"/>
<font color="Maroon" title="c3">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c4">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c5">c'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="cat_1.html#E1:105"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="cat_1.html#T124" target="_self" title="CAT_1:th.124">Th124</a></i>;<br/>
<b>hence </b><a NAME="E3:105"/>
<font color="Maroon" title="c3">T</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">T</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c5">c'</font>
 <b>by </b><i><a class="ref" href="cat_1.html#D7" target="_self" title="CAT_1:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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