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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:12_1_1_1"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_3.html#V4">yielding_non-empty_carriers</a>
 ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E2:12_1_1_1"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E3:12_1_1_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>hence </b><a NAME="E4:12_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> 
 <b>by </b><i><a class="txt" href="yellow_6.html#E1:12_1_1_1"><i><font color="Green">E6</font></i></a>, <a class="txt" href="yellow_6.html#E2:12_1_1_1"><i><font color="Green">E7</font></i></a>, <a class="ref" href="pralg_1.html#D11">PRALG_1:def 11</a>, <a class="ref" href="waybel_3.html#D7">WAYBEL_3:def 7</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:12_1_1"/><i><font color="Green">E6</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> 
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="struct_0.html#L1">1-sorted</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D7">WAYBEL_3:def 7</a><br/>

<b>thus </b><a NAME="E3:12_1_1"/>
(  not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font> or  not <font color="Maroon">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a> )
 <b>by </b><i><a class="txt" href="yellow_6.html#E2:12_1_1"><i><font color="Green">E6</font></i></a></i>;<br/>


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