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<span class="kw">let </span><font color="Maroon" title="c1">p</font> be   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">d1</font>, <font color="Olive" title="b4">Y1</font>, <font color="Olive" title="b5">d2</font>, <font color="Olive" title="b6">Y2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span>  st <font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3 &amp;  <a href="ec_pf_1.html#K4" title="EC_PF_1:func.4">Disc</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c1">p</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span> &amp; <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Olive" title="b3">d1</font>,<font color="Olive" title="b4">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ec_pf_1.html#K6" title="EC_PF_1:func.6">EC_SetProjCo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c1">p</font>) &amp; <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Olive" title="b5">d2</font>,<font color="Olive" title="b6">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ec_pf_1.html#K6" title="EC_PF_1:func.6">EC_SetProjCo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c1">p</font>) holds <br/>(  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Olive" title="b3">d1</font>,<font color="Olive" title="b4">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Olive" title="b5">d2</font>,<font color="Olive" title="b6">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) iff ( <font color="Olive" title="b3">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">d2</font> &amp; <font color="Olive" title="b4">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">Y2</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">d1</font>, <font color="Maroon" title="c5">Y1</font>, <font color="Maroon" title="c6">d2</font>, <font color="Maroon" title="c7">Y2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span>; <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="c1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3 &amp;  <a href="ec_pf_1.html#K4" title="EC_PF_1:func.4">Disc</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span> &amp; <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ec_pf_1.html#K6" title="EC_PF_1:func.6">EC_SetProjCo</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>) &amp; <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ec_pf_1.html#K6" title="EC_PF_1:func.6">EC_SetProjCo</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>) implies (  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) iff ( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d2</font> &amp; <font color="Maroon" title="c5">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">Y2</font> ) ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:81"/><span class="lab"><font color="Green" title="E60">AS</font></span>: 
( <font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3 &amp;  <a href="ec_pf_1.html#K4" title="EC_PF_1:func.4">Disc</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span> &amp; <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ec_pf_1.html#K6" title="EC_PF_1:func.6">EC_SetProjCo</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>) &amp; <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ec_pf_1.html#K6" title="EC_PF_1:func.6">EC_SetProjCo</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) iff ( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d2</font> &amp; <font color="Maroon" title="c5">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">Y2</font> ) )</span><br/>

<div><span class="kw">hereby </span> <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="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d2</font> &amp; <font color="Maroon" title="c5">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">Y2</font> implies  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:81_1"/>
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>)
 ; <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="c6">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">d1</font> &amp; <font color="Maroon" title="c7">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Y1</font> )</span><br/><a NAME="E2:81_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81"><span class="lab"><font color="Green" title="E60">AS</font></span></a>, <a class="ref" href="eqrel_1.html#T23" title="EQREL_1:th.23">EQREL_1:23</a></span>;<br/><a NAME="E3:81_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">P07</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>,<span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T18" title="EQREL_1:th.18">EQREL_1:18</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c8">P</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>, <font color="Maroon" title="c9">Q</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ec_pf_1.html#K3" title="EC_PF_1:func.3">ProjCo</a> <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:81"><span class="lab"><font color="Green" title="E60">AS</font></span></a></span>;<br/><a NAME="E5:81_1"/>
<font color="Maroon" title="c8">P</font> <a href="ec_pf_1.html#R1" title="EC_PF_1:pred.1">_EQ_</a> <font color="Maroon" title="c9">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#T50" target="_self" title="EC_PF_1:th.50">LmDefREQ0</a>, <a class="txt" href="#E1:81"><span class="lab"><font color="Green" title="E60">AS</font></span></a>, <a class="txt" href="#E3:81_1"><span class="lab"><font color="Green" title="E61">P07</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E7:81_1"/><span class="lab"><font color="Green" title="E62">P08</font></span>: 
( <font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span> &amp; <font color="Maroon" title="c9">Q</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">P</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> &amp; <font color="Maroon" title="c9">Q</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">P</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> &amp; <font color="Maroon" title="c9">Q</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#D10" target="_self" title="EC_PF_1:def.10">DefEQV</a></span>;<br/><a NAME="E8:81_1"/><span class="lab"><font color="Green" title="E63">PP1</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#D4" title="INT_2:def.4">INT_2:def 4</a></span>;<br/><span class="lab"><font color="Green" title="E64">P09</font></span>:  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span> = 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:81_1"><span class="lab"><font color="Green" title="E63">PP1</font></span></a>, <a class="ref" href="int_3.html#T14" title="INT_3:th.14">INT_3:14</a></span>
<br/>.= 
<font color="Maroon" title="c8">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T43" title="MCART_1:th.43">MCART_1:43</a></span>
;<br/><span class="lab"><font color="Green" title="E65">P10</font></span>:  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span> = 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:81_1"><span class="lab"><font color="Green" title="E63">PP1</font></span></a>, <a class="ref" href="int_3.html#T14" title="INT_3:th.14">INT_3:14</a></span>
<br/>.= 
<font color="Maroon" title="c10">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:81_1"><span class="lab"><font color="Green" title="E62">P08</font></span></a>, <a class="ref" href="mcart_1.html#T43" title="MCART_1:th.43">MCART_1:43</a></span>
<br/>.= 
<font color="Maroon" title="c10">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:81_1"><span class="lab"><font color="Green" title="E64">P09</font></span></a>, <a class="ref" href="vectsp_1.html#D8" title="VECTSP_1:def.8">VECTSP_1:def 8</a></span>
;<br/><span class="kw">thus </span><font color="Maroon" title="c6">d2</font> = 
<font color="Maroon" title="c10">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">P</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:81_1"><span class="lab"><font color="Green" title="E62">P08</font></span></a>, <a class="ref" href="mcart_1.html#T43" title="MCART_1:th.43">MCART_1:43</a></span>
<br/>.= 
<font color="Maroon" title="c8">P</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:81_1"><span class="lab"><font color="Green" title="E65">P10</font></span></a>, <a class="ref" href="vectsp_1.html#D8" title="VECTSP_1:def.8">VECTSP_1:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c4">d1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T43" title="MCART_1:th.43">MCART_1:43</a></span>
; <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="c7">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Y1</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c7">Y2</font> = 
<font color="Maroon" title="c10">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">P</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:81_1"><span class="lab"><font color="Green" title="E62">P08</font></span></a>, <a class="ref" href="mcart_1.html#T43" title="MCART_1:th.43">MCART_1:43</a></span>
<br/>.= 
<font color="Maroon" title="c8">P</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:81_1"><span class="lab"><font color="Green" title="E65">P10</font></span></a>, <a class="ref" href="vectsp_1.html#D8" title="VECTSP_1:def.8">VECTSP_1:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c5">Y1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T43" title="MCART_1:th.43">MCART_1:43</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/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E3:81"/>
( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d2</font> &amp; <font color="Maroon" title="c5">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">Y2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>)</span><br/>

<span class="kw">hence </span><a NAME="E4:81"/>
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">d1</font>,<font color="Maroon" title="c5">Y1</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ec_pf_1.html#K8" title="EC_PF_1:func.8">R_EllCur</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span>,<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">d2</font>,<font color="Maroon" title="c7">Y2</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</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/>


</div>
