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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="struct_0.html#L1">1-sorted</a> ;<br/>

<b>assume </b><a NAME="E1:5_1_1"/><i><font color="Green">E1</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:5_1_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> or  not <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_1_1_1"><b>suppose </b></a><a NAME="E1:5_1_1_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a>  ;<br/><a NAME="E3:5_1_1_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/><b>hence </b><a NAME="E4:5_1_1_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D14">GROUP_1:def 14</a><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_1_1_2"><b>suppose </b></a><a NAME="E1:5_1_1_1_2"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="struct_0.html#V3">empty</a> <a href="realset2.html#V3">trivial</a>  <a href="struct_0.html#L1">1-sorted</a>  <b>by </b><i><a class="txt" href="yellow13.html#E1:5_1_1"><i><font color="Green">E1</font></i></a></i>;<br/><a NAME="E3:5_1_1_1_2"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/><b>hence </b><a NAME="E4:5_1_1_1_2"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D14">GROUP_1:def 14</a><br/></div><b>end;</b></div></div><b>end;</b></div>

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