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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:15_1"/>
<font color="Maroon" title="c1">T</font> is <a href="borsuk_6.html#V1" title="BORSUK_6:attr.1">real-membered</a>
 ;<br/><a NAME="E2:15_1"/><b>then </b><i><font color="Green" title="E17">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="membered.html#V2" title="MEMBERED:attr.2">real-membered</a>
 <b>by </b><i><a class="ref" href="borsuk_6.html#D1" target="_self" title="BORSUK_6:def.1">Def1</a></i>;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>;<br/><b>thus </b><a NAME="E3:15_1"/>
<font color="Maroon" title="c2">x</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>
 <b>by </b><i><a class="txt" href="borsuk_6.html#E2:15_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="membered.html#D2" title="MEMBERED:def.2">MEMBERED:def 2</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:15"/>
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Olive" title="b1">x</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>
 ;<br/>

<a NAME="E3:15"/><b>then </b>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> holds <br/><font color="Olive" title="b1">x</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>
 
;<br/>
<a NAME="E4:15"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="membered.html#V2" title="MEMBERED:attr.2">real-membered</a>
 
<b>by </b><i><a class="ref" href="membered.html#D2" title="MEMBERED:def.2">MEMBERED:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/>
<font color="Maroon" title="c1">T</font> is <a href="borsuk_6.html#V1" title="BORSUK_6:attr.1">real-membered</a>
 <b>by </b><i><a class="ref" href="borsuk_6.html#D1" target="_self" title="BORSUK_6:def.1">Def1</a></i>;<br/>


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