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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c1">L</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font></span>)</span>)</span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K3" title="POLYNOM8:func.3">mConv</a> (<span class="p3">(<span class="default"><font color="Olive" title="b2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b3">q</font></span>)</span>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="matrix_3.html#K15" title="MATRIX_3:func.15">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K3" title="POLYNOM8:func.3">mConv</a> (<span class="p2">(<span class="default"><font color="Olive" title="b2">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b3">q</font></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b1">m</font></span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c1">L</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K3" title="POLYNOM8:func.3">mConv</a> (<span class="p3">(<span class="default"><font color="Olive" title="b1">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b2">q</font></span>)</span>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="matrix_3.html#K15" title="MATRIX_3:func.15">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K3" title="POLYNOM8:func.3">mConv</a> (<span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b2">q</font></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:59"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c1">L</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K3" title="POLYNOM8:func.3">mConv</a> (<span class="p3">(<span class="default"><font color="Olive" title="b1">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b2">q</font></span>)</span>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="matrix_3.html#K15" title="MATRIX_3:func.15">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K3" title="POLYNOM8:func.3">mConv</a> (<span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b2">q</font></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c1">L</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K3" title="POLYNOM8:func.3">mConv</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="matrix_3.html#K15" title="MATRIX_3:func.15">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K3" title="POLYNOM8:func.3">mConv</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span></span><br/>

<a NAME="E2:59"/>
2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="xreal_1.html#T68" onmouseover="rs('xreal_1/T68')" onmouseout="rh()">XREAL_1:68</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:59"/>
<span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K3" title="MATRIX_1:func.3">1.</a> (<font color="Maroon" title="c1">L</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="polynom8.html#K3" title="POLYNOM8:func.3">mConv</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom8.html#K1" title="POLYNOM8:func.1">emb</a> (<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span> <a href="matrix_3.html#K15" title="MATRIX_3:func.15">*</a> <span class="p1">(<span class="default"><a href="polynom8.html#K3" title="POLYNOM8:func.3">mConv</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c4">q</font></span>)</span>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c2">m</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom8.html#T35" target="_self" onmouseover="rs('polynom8/T35')" onmouseout="rh()">Th35</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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