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

<b>let </b><font color="Maroon" title="c1">V</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">g</font>, <font color="Olive" title="b2">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">V</font></span>)</span>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b2">f</font> holds <br/><font color="Olive" title="b1">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Olive" title="b1">g</font></span>)</span> <a href="ens_1.html#K6" title="ENS_1:func.6">*</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Olive" title="b2">f</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">g</font>, <font color="Maroon" title="c3">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">V</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font> implies <font color="Maroon" title="c2">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="ens_1.html#K6" title="ENS_1:func.6">*</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c3">f</font></span>)</span> )</span><br/>





<b>assume </b><a NAME="E1:47"/><i><font color="Green" title="E32">A1</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="ens_1.html#K6" title="ENS_1:func.6">*</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c3">f</font></span>)</span></span><br/>

<a NAME="E2:47"/><b>then </b>
 <a href="ens_1.html#K3" title="ENS_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font>
 
<b>by </b><i><a class="ref" href="ens_1.html#D10" target="_self" title="ENS_1:def.10">Def10</a></i>;<br/>
<a NAME="E3:47"/><b>then </b><i><font color="Green" title="E33">A2</font></i>: 
 <a href="ens_1.html#K3" title="ENS_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ens_1.html#K4" title="ENS_1:func.4">cod</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c3">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ens_1.html#D11" target="_self" title="ENS_1:def.11">Def11</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c2">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font> = 
the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</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">V</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">f</font>
<b>by </b><i><a class="txt" href="ens_1.html#E1:47"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="cat_1.html#T41" title="CAT_1:th.41">CAT_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="ens_1.html#K6" title="ENS_1:func.6">*</a> <span class="p1">(<span class="default"><a href="ens_1.html#K16" title="ENS_1:func.16">@</a> <font color="Maroon" title="c3">f</font></span>)</span>
<b>by </b><i><a class="txt" href="ens_1.html#E3:47"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="ens_1.html#D12" target="_self" title="ENS_1:def.12">Def12</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
