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<b>let </b><font color="Maroon" title="c1">C</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="altcat_1.html#V12" title="ALTCAT_1:attr.12">with_units</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">o</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>;<br/>



<b>thus </b><a NAME="E1:5"/>
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c2">o</font> is <a href="altcat_3.html#V5" title="ALTCAT_3:attr.5">epi</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">o1</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D8" title="ALTCAT_3:def.8">ALTCAT_3:def 8</a><br/>

<b>assume </b><a NAME="E1:5_1"/><i><font color="Green" title="E5">A1</font></i>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></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> 
 ;<br/>

<b>let </b><font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">C</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">o1</font>;<br/>

<b>assume </b><a NAME="E2:5_1"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c4">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c2">o</font></span>)</span>
 ;<br/>

<b>thus </b><font color="Maroon" title="c4">B</font> = 
<font color="Maroon" title="c4">B</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c2">o</font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_4.html#E1:5_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="altcat_1.html#D19" title="ALTCAT_1:def.19">ALTCAT_1:def 19</a></i>
<br/>.= 
<font color="Maroon" title="c5">C</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E1:5_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="altcat_4.html#E2:5_1"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="altcat_1.html#D19" title="ALTCAT_1:def.19">ALTCAT_1:def 19</a></i>
;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c3">o1</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D7" title="ALTCAT_3:def.7">ALTCAT_3:def 7</a><br/>

<b>assume </b><a NAME="E2:5"/><i><font color="Green" title="E5">A3</font></i>: 
<span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c2">o</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></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> 
 ;<br/>

<b>let </b><font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">C</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c2">o</font>;<br/>

<b>assume </b><a NAME="E3:5"/><i><font color="Green" title="E6">A4</font></i>: 
<span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">C</font>
 ;<br/>

<b>thus </b><font color="Maroon" title="c4">B</font> = 
<span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c2">o</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c4">B</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E2:5"><i><font color="Green" title="E5">A3</font></i></a>, <a class="ref" href="altcat_1.html#T24" title="ALTCAT_1:th.24">ALTCAT_1:24</a></i>
<br/>.= 
<font color="Maroon" title="c5">C</font>
<b>by </b><i><a class="txt" href="altcat_4.html#E2:5"><i><font color="Green" title="E5">A3</font></i></a>, <a class="txt" href="altcat_4.html#E3:5"><i><font color="Green" title="E6">A4</font></i></a>, <a class="ref" href="altcat_1.html#T24" title="ALTCAT_1:th.24">ALTCAT_1:24</a></i>
;<br/>


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