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<span class="kw">let </span><font color="Maroon" title="c2">C</font> be   <a href="cat_6.html#V9" title="CAT_6:attr.9">composable</a>   <a href="cat_6.html#V10" title="CAT_6:attr.10">with_identities</a>   <a href="cat_6.html#L1" title="CAT_6:struct.1">CategoryStr</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> is <font color="Maroon" title="c1">O</font> <a href="cat_7.html#V7" title="CAT_7:attr.7">-ordered</a>  implies <font color="Maroon" title="c2">C</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:64_1_1"/>
<font color="Maroon" title="c2">C</font> is <font color="Maroon" title="c1">O</font> <a href="cat_7.html#V7" title="CAT_7:attr.7">-ordered</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">C</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">F</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E3:64_1_1"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="wellord1.html#R3" title="WELLORD1:pred.3">is_isomorphism_of</a>  <a href="cat_7.html#K5" title="CAT_7:func.5">RelOb</a> <font color="Maroon" title="c2">C</font>, <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">O</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="wellord1.html#D8" onmouseover="rs('wellord1/D8')" onmouseout="rh()">WELLORD1:def 8</a></span>;<br/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">F</font> = 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">O</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:64_1_1"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="wellord1.html#D7" onmouseover="rs('wellord1/D7')" onmouseout="rh()">WELLORD1:def 7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p2">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">O</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <span class="p2">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">O</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D6" onmouseover="rs('relat_1/D6')" onmouseout="rh()">RELAT_1:def 6</a></span>
<br/>.= 
<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <span class="p2">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">O</font></span>)</span></span>)</span>

<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 

;<br/>
<a NAME="E5:64_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A2</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<a NAME="E6:64_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <span class="p1">(<span class="default"><a href="cat_7.html#K5" title="CAT_7:func.5">RelOb</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:64_1_1"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="wellord1.html#D7" onmouseover="rs('wellord1/D7')" onmouseout="rh()">WELLORD1:def 7</a></span>;<br/>
<a NAME="E7:64_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="cat_7.html#K5" title="CAT_7:func.5">RelOb</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="cat_7.html#K5" title="CAT_7:func.5">RelOb</a> <font color="Maroon" title="c2">C</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:64_1_1"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="relat_1.html#D6" onmouseover="rs('relat_1/D6')" onmouseout="rh()">RELAT_1:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:64_1_1"/>
<font color="Maroon" title="c2">C</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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