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

<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</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">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  &amp; <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  implies <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  )</span><br/>







<b>assume </b><a NAME="E1:72"/><i><font color="Green" title="E36">A1</font></i>: 
 <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">b</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> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D17" target="_self" title="CAT_1:def.17">CAT_1:def 17</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#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>  holds not <font color="Olive" title="b1">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a> or  not <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  or <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  )</span><br/>

<b>given </b><font color="Maroon" title="c5">f</font> being    <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">b</font><b> such that </b><a NAME="E3:72"/><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c5">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  or <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  )</span><br/>

<b>assume </b><a NAME="E4:72"/><i><font color="Green" title="E38">A3</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">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> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D17" target="_self" title="CAT_1:def.17">CAT_1:def 17</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#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>  holds not <font color="Olive" title="b1">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a> or <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a>  )</span><br/>

<b>given </b><font color="Maroon" title="c6">g</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font><b> such that </b><a NAME="E6:72"/><i><font color="Green" title="E39">A4</font></i>: 
<font color="Maroon" title="c6">g</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="cat_1.html#R1" title="CAT_1:pred.1">are_isomorphic</a> </span><br/>

<b>thus </b><a NAME="E7:72"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">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>by </b><i><a class="txt" href="#E1:72"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="#E4:72"><i><font color="Green" title="E38">A3</font></i></a>, <a class="ref" href="cat_1.html#T51" target="_self" title="CAT_1:th.51">Th51</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D17" target="_self" title="CAT_1:def.17">CAT_1:def 17</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">f</font> being   <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="c4">c</font> st <font color="Olive" title="b1">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a></span><br/>

<b>take </b>
<font color="Maroon" title="c6">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">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="c6">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a></span><br/>

<b>thus </b><a NAME="E8:72"/>
<font color="Maroon" title="c6">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a>
 <b>by </b><i><a class="txt" href="#E1:72"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="#E3:72"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="#E4:72"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="#E6:72"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="cat_1.html#T75" target="_self" title="CAT_1:th.75">Th75</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>
