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<b>let </b><font color="Maroon" title="c1">o</font>, <font color="Maroon" title="c2">m</font> be    <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">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> holds  <font color="Olive" title="b1">a</font> is <a href="cat_1.html#V7" title="CAT_1:attr.7">terminal</a></span><br/><b>let </b><font color="Maroon" title="c3">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</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="c3">a</font> is <a href="cat_1.html#V7" title="CAT_1:attr.7">terminal</a></span><br/><b>let </b><font color="Maroon" title="c4">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D15" title="CAT_1:def.15">CAT_1:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  ex <font color="Olive">b<sub>1</sub></font> being   <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="c3">a</font> st <br/>for <font color="Olive">b<sub>2</sub></font> being   <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="c3">a</font> holds  <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> )</span><br/>







<b>thus </b><a NAME="E1:17"/>
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">a</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="ref" href="cat_4.html#T7" target="_self" title="CAT_4:th.7">Th7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <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="c3">a</font> st <br/>for <font color="Olive">b<sub>2</sub></font> being   <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="c3">a</font> holds  <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font></span><br/>

<b>consider </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="c4">b</font>,<font color="Maroon" title="c3">a</font>;<br/>
<b>take </b>
<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"> for <font color="Olive">b<sub>1</sub></font> being   <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="c3">a</font> holds  <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font></span><br/>

<b>thus </b><a NAME="E3:17"/>
for <font color="Olive">b<sub>1</sub></font> being   <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="c3">a</font> holds  <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="cat_4.html#T6" target="_self" title="CAT_4:th.6">Th6</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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