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<b>let </b><font color="Maroon" title="c1">W</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</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#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="ens_1.html#K12" title="ENS_1:func.12">Ens</a> <font color="Maroon" title="c1">W</font></span>)</span>  st <font color="Olive" title="b1">f</font> is <a href="cat_1.html#V4" title="CAT_1:attr.4">epi</a> holds <br/> <a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Olive" title="b1">f</font> is <a href="ens_1.html#V1" title="ENS_1:attr.1">surjective</a></span><br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="ens_1.html#K12" title="ENS_1:func.12">Ens</a> <font color="Maroon" title="c1">W</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> is <a href="cat_1.html#V4" title="CAT_1:attr.4">epi</a> implies  <a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c2">f</font> is <a href="ens_1.html#V1" title="ENS_1:attr.1">surjective</a> )</span><br/>



<a NAME="E1:55"/><i><font color="Green" title="E35">A1</font></i>: 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font>
 
<b>by </b><i><a class="ref" href="classes2.html#T62" title="CLASSES2:th.62">CLASSES2:62</a></i>;<br/>
<a NAME="E2:55"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font>
 
<b>by </b><i><a class="ref" href="classes2.html#T62" title="CLASSES2:th.62">CLASSES2:62</a>, <a class="ref" href="classes2.html#T63" title="CLASSES2:th.63">CLASSES2:63</a></i>;<br/>
<a NAME="E3:55"/><b>then </b>
( <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</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>  )
 
<b>by </b><i><a class="txt" href="#E1:55"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="classes2.html#T64" title="CLASSES2:th.64">CLASSES2:64</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:55"/>
( <font color="Maroon" title="c2">f</font> is <a href="cat_1.html#V4" title="CAT_1:attr.4">epi</a> implies  <a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c2">f</font> is <a href="ens_1.html#V1" title="ENS_1:attr.1">surjective</a> )
 <b>by </b><i><a class="ref" href="ens_1.html#T37" target="_self" title="ENS_1:th.37">Th37</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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