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<span class="kw">let </span><font color="Maroon" title="c2">b</font> be   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">b</font> is  <a href="polynom7.html#V2" title="POLYNOM7:attr.2">univariate</a>  implies  not <font color="Maroon" title="c2">b</font> is  <a href="polynom2.html#V1" title="POLYNOM2:attr.1">empty</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:9_1_1"/>
<font color="Maroon" title="c2">b</font> is  <a href="polynom7.html#V2" title="POLYNOM7:attr.2">univariate</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c2">b</font> is  <a href="polynom2.html#V1" title="POLYNOM2:attr.1">empty</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:9_1_1"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
 <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D2" target="_self" title="POLYNOM7:def.2">Def3</a></span>;<br/>
<a NAME="E4:9_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:9_1_1"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E5:9_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D7" title="PRE_POLY:def.7">PRE_POLY:def 7</a></span>;<br/>
<a NAME="E6:9_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T52" title="PRE_POLY:th.52">PRE_POLY:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:9_1_1"/>
 not <font color="Maroon" title="c2">b</font> is  <a href="polynom2.html#V1" title="POLYNOM2:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom2.html#D1" title="POLYNOM2:def.1">POLYNOM2:def 1</a></span>; <a class="txt" 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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