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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="algstr_0.html#L5" title="ALGSTR_0:struct.5">multLoopStr_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">z</font> being    <a href="ratfunc1.html#M1" title="RATFUNC1:mode.1">rational_function</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="ratfunc1.html#K3" title="RATFUNC1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">z</font> <a href="ratfunc1.html#K4" title="RATFUNC1:func.4">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">z</font> <a href="ratfunc1.html#K5" title="RATFUNC1:func.5">`2</a></span>)</span></span><a href="ratfunc1.html#K3" title="RATFUNC1:func.3">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">z</font> be    <a href="ratfunc1.html#M1" title="RATFUNC1:mode.1">rational_function</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"> <font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="ratfunc1.html#K3" title="RATFUNC1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="ratfunc1.html#K4" title="RATFUNC1:func.4">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="ratfunc1.html#K5" title="RATFUNC1:func.5">`2</a></span>)</span></span><a href="ratfunc1.html#K3" title="RATFUNC1:func.3">]</a></span></span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">p1</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font><span class="kw"> such that </span><br/><a NAME="E2:53"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 ex <font color="Olive" title="b1">p2</font> being   non  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font> st <font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="ratfunc1.html#K3" title="RATFUNC1:func.3">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Olive" title="b1">p2</font></span><a href="ratfunc1.html#K3" title="RATFUNC1:func.3">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ratfunc1.html#D8" target="_self" onmouseover="rs('ratfunc1/D8')" onmouseout="rh()">Def8</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">p2</font> being   non  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font><span class="kw"> such that </span><br/><a NAME="E4:53"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="ratfunc1.html#K3" title="RATFUNC1:func.3">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font></span><a href="ratfunc1.html#K3" title="RATFUNC1:func.3">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:53"><span class="lab"><font color="Green" title="E17">A1</font></span></a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:53"/>
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="ratfunc1.html#K3" title="RATFUNC1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="ratfunc1.html#K4" title="RATFUNC1:func.4">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="ratfunc1.html#K5" title="RATFUNC1:func.5">`2</a></span>)</span></span><a href="ratfunc1.html#K3" title="RATFUNC1:func.3">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:53"><span class="lab"><font color="Green" title="E18">A2</font></span></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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