<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="cat_4.html#NM2" title="CAT_4:NM.2">Cocartesian_category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">d</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#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</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>  &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">d</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/> <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Olive" title="b3">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">c</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Olive" title="b4">d</font></span>)</span> <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><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">d</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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>  &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">d</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  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c4">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c5">d</font></span>)</span> <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><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:108"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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> 
 <span class="kw">and </span><br/><a NAME="E2:108"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">d</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="Red">::  thesis: </font></span></a><span class="hide">  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c4">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c5">d</font></span>)</span> <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><br/>

<a NAME="E3:108"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c5">d</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c5">d</font></span>)</span> <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_4.html#T66" target="_self" title="CAT_4:th.66">Th66</a></span>;<br/>
<a NAME="E4:108"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A3</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c4">b</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c5">d</font></span>)</span> <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="txt" href="#E2:108"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="cat_1.html#T52" title="CAT_1:th.52">CAT_1:52</a></span>;<br/>
<a NAME="E5:108"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c5">d</font></span>)</span> <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_4.html#T66" target="_self" title="CAT_4:th.66">Th66</a></span>;<br/>
<a NAME="E6:108"/><span class="kw">then </span>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c5">d</font></span>)</span> <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="txt" href="#E1:108"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="cat_1.html#T52" title="CAT_1:th.52">CAT_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:108"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c4">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c5">d</font></span>)</span> <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="txt" href="#E4:108"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="cat_4.html#T70" target="_self" title="CAT_4:th.70">Th70</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/>


</div>
