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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="cat_4.html#NM2" title="CAT_4:NM.2">Cocartesian_category</a>;<br/><b>let </b><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>, <font color="Maroon" title="c6">e</font>, <font color="Maroon" title="c7">s</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>;<br/><b>let </b><font color="Maroon" title="c8">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">c</font>;<br/><b>let </b><font color="Maroon" title="c9">h</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">d</font>;<br/><b>let </b><font color="Maroon" title="c10">g</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">e</font>;<br/><b>let </b><font color="Maroon" title="c11">k</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">s</font>;<br/>





















<b>assume </b><b>that </b><br/><a NAME="E1:106"/><i><font color="Green" title="E49">A1</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">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> 
 <b>and </b><br/><a NAME="E2:106"/><i><font color="Green" title="E50">A2</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">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> 
 <b>and </b><br/><a NAME="E3:106"/><i><font color="Green" title="E51">A3</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">e</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>and </b><br/><a NAME="E4:106"/><i><font color="Green" title="E52">A4</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c7">s</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> 
 ;<br/>

<a NAME="E5:106"/><i><font color="Green" title="E53">A5</font></i>: 
(  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c6">e</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">e</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c7">s</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>  &amp;  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c7">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">e</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c7">s</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>  )
 
<b>by </b><i><a class="ref" href="cat_4.html#T66" target="_self" title="CAT_4:th.66">Th66</a></i>;<br/>
<a NAME="E6:106"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K25" title="CAT_4:func.25">in1</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c10">g</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K25" title="CAT_4:func.25">in1</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c8">f</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K26" title="CAT_4:func.26">in2</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c11">k</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K26" title="CAT_4:func.26">in2</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c9">h</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="cat_4.html#E1:106"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="cat_4.html#E2:106"><i><font color="Green" title="E50">A2</font></i></a>, <a class="txt" href="cat_4.html#E3:106"><i><font color="Green" title="E51">A3</font></i></a>, <a class="txt" href="cat_4.html#E4:106"><i><font color="Green" title="E52">A4</font></i></a>, <a class="ref" href="cat_1.html#T54" title="CAT_1:th.54">CAT_1:54</a></i>;<br/>
<a NAME="E7:106"/><b>then </b>
(  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">e</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c7">s</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>  &amp;  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c5">d</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">e</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c7">s</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>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c8">f</font></span>)</span> <a href="cat_4.html#K29" title="CAT_4:func.29">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c9">h</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_4.html#K27" title="CAT_4:func.27">[$</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_4.html#K25" title="CAT_4:func.25">in1</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c10">g</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c8">f</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_4.html#K26" title="CAT_4:func.26">in2</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c11">k</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c9">h</font></span>)</span></span><a href="cat_4.html#K27" title="CAT_4:func.27">$]</a></span> &amp; <font color="Maroon" title="c10">g</font> <a href="cat_4.html#K29" title="CAT_4:func.29">+</a> <font color="Maroon" title="c11">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_4.html#K27" title="CAT_4:func.27">[$</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_4.html#K25" title="CAT_4:func.25">in1</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c10">g</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_4.html#K26" title="CAT_4:func.26">in2</a> <font color="Maroon" title="c6">e</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c11">k</font></span>)</span></span><a href="cat_4.html#K27" title="CAT_4:func.27">$]</a></span> )
 
<b>by </b><i><a class="txt" href="cat_4.html#E3:106"><i><font color="Green" title="E51">A3</font></i></a>, <a class="txt" href="cat_4.html#E4:106"><i><font color="Green" title="E52">A4</font></i></a>, <a class="txt" href="cat_4.html#E5:106"><i><font color="Green" title="E53">A5</font></i></a>, <a class="ref" href="cat_1.html#T52" title="CAT_1:th.52">CAT_1:52</a></i>;<br/>
<b>hence </b><a NAME="E8:106"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="cat_4.html#K29" title="CAT_4:func.29">+</a> <font color="Maroon" title="c11">k</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="cat_4.html#K29" title="CAT_4:func.29">+</a> <font color="Maroon" title="c9">h</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">g</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c8">f</font></span>)</span> <a href="cat_4.html#K29" title="CAT_4:func.29">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c9">h</font></span>)</span>
 <b>by </b><i><a class="txt" href="cat_4.html#E1:106"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="cat_4.html#E2:106"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="cat_4.html#T80" target="_self" title="CAT_4:th.80">Th80</a></i>;<br/>


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