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<b>let </b><font color="Maroon">L1</font> be    <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">L2</font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L1</font>,<font color="Maroon">L2</font>;<br/>



<b>assume </b><a NAME="E1:15"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">f</font> is <a href="waybel_0.html#V23">isomorphic</a>
 ;<br/>

<a NAME="E2:15"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  iff the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>proof </b></a><div class="add">

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:15_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:15_1_1"/><b>then </b>
<font color="Maroon">L1</font> is <a href="struct_0.html#V3">empty</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/><a NAME="E3:15_1_1"/><b>then </b>
<font color="Maroon">L2</font> is <a href="struct_0.html#V3">empty</a>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/><b>hence </b><a NAME="E4:15_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:15_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E3:15_1"/><b>then </b>
<font color="Maroon">L2</font> is <a href="struct_0.html#V3">empty</a>
 
<b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>
<a NAME="E4:15_1"/><b>then </b>
<font color="Maroon">L1</font> is <a href="struct_0.html#V3">empty</a>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:15"/>
( ( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  implies the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; ( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  implies the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; ( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  or the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; ( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; ( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) )
 ;<br/>


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