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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="cat_4.html#NM1" title="CAT_4:NM.1">Cartesian_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">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="c1">C</font><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>  st  <a href="cat_1.html#K7" title="CAT_1:func.7">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/><span class="p1"><a href="cat_4.html#K9" title="CAT_4:func.9">&lt;:</a><span class="default"><font color="Olive" title="b3">f</font>,<font color="Olive" title="b3">f</font></span><a href="cat_4.html#K9" title="CAT_4:func.9">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K15" title="CAT_4:func.15">Delta</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b3">f</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</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"> 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="c2">a</font>,<font color="Maroon" title="c3">b</font>  st  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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/><span class="p1"><a href="cat_4.html#K9" title="CAT_4:func.9">&lt;:</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Olive" title="b1">f</font></span><a href="cat_4.html#K9" title="CAT_4:func.9">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K15" title="CAT_4:func.15">Delta</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Olive" title="b1">f</font></span><br/><b>let </b><font color="Maroon" title="c4">f</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</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="c2">a</font>,<font color="Maroon" title="c3">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 <span class="p1"><a href="cat_4.html#K9" title="CAT_4:func.9">&lt;:</a><span class="default"><font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c4">f</font></span><a href="cat_4.html#K9" title="CAT_4:func.9">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K15" title="CAT_4:func.15">Delta</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c4">f</font> )</span><br/>







<b>assume </b><a NAME="E1:51"/><i><font color="Green" title="E25">A1</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="cat_4.html#K9" title="CAT_4:func.9">&lt;:</a><span class="default"><font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c4">f</font></span><a href="cat_4.html#K9" title="CAT_4:func.9">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K15" title="CAT_4:func.15">Delta</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c4">f</font></span><br/>

<a NAME="E2:51"/><i><font color="Green" title="E26">A2</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">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> 
 
<b>by </b><i><a class="ref" href="cat_1.html#T56" title="CAT_1:th.56">CAT_1:56</a></i>;<br/>
<a NAME="E3:51"/>
<span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="cat_4.html#E1:51"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="cat_1.html#T57" title="CAT_1:th.57">CAT_1:57</a></i>;<br/>
<b>hence </b><a NAME="E4:51"/>
<span class="p1"><a href="cat_4.html#K9" title="CAT_4:func.9">&lt;:</a><span class="default"><font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c4">f</font></span><a href="cat_4.html#K9" title="CAT_4:func.9">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K15" title="CAT_4:func.15">Delta</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="cat_4.html#E1:51"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="cat_4.html#E2:51"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="cat_4.html#T27" target="_self" title="CAT_4:th.27">Th27</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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