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<b>let </b><font color="Maroon" title="c1">a</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">b</font> being <a href="seq_1.html#NV1" title="SEQ_1:NV.1">real-yielding</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Olive" title="b1">X</font>  st <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Olive" title="b2">b</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b</font> being <a href="seq_1.html#NV1" title="SEQ_1:NV.1">real-yielding</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c2">X</font>  st <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Olive" title="b1">b</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">b</font> be  <a href="seq_1.html#NV1" title="SEQ_1:NV.1">real-yielding</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c2">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c3">b</font></span>)</span> )</span><br/>





<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">b</font></span>
<div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">b</font> implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c3">b</font></span>)</span> )</span><br/><b>assume </b><a NAME="E1:30_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/><a NAME="E2:30_1"/><b>then </b>
<font color="Maroon" title="c3">b</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">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> 
 <b>by </b><i><a class="ref" href="polynom1.html#D7" title="POLYNOM1:def.7">POLYNOM1:def 7</a></i>;<br/><a NAME="E3:30_1"/><b>then </b>
<font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="nat_3.html#E1:30"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="xcmplx_1.html#T6" title="XCMPLX_1:th.6">XCMPLX_1:6</a></i>;<br/><a NAME="E4:30_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">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> 
 <b>by </b><i><a class="ref" href="nat_3.html#D2" target="_self" title="NAT_3:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E5:30_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D7" title="POLYNOM1:def.7">POLYNOM1:def 7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c3">b</font></span>)</span> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">b</font> )</span><br/>

<b>assume </b><a NAME="E3:30"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c3">b</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">b</font></span><br/>

<a NAME="E4:30"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">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> 
 
<b>by </b><i><a class="ref" href="polynom1.html#D7" title="POLYNOM1:def.7">POLYNOM1:def 7</a></i>;<br/>
<a NAME="E5:30"/><b>then </b>
<font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="nat_3.html#D2" target="_self" title="NAT_3:def.2">Def2</a></i>;<br/>
<a NAME="E6:30"/><b>then </b>
<font color="Maroon" title="c3">b</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">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> 
 
;<br/>
<b>hence </b><a NAME="E7:30"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D7" title="POLYNOM1:def.7">POLYNOM1:def 7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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