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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> 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><br/>  for <font color="Olive" title="b3">F1</font>, <font color="Olive" title="b4">F2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   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; <font color="Olive" title="b3">F1</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"><span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p3">(<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="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Olive" title="b4">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p3">(<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>,<font color="Olive" title="b5">P</font>)</span>)</span> where <font color="Olive" title="b5">P</font> is    <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> : ( <font color="Olive" title="b5">P</font> <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;  ex <font color="Olive" title="b6">X</font>, <font color="Olive" title="b7">Y</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="Olive" title="b5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Olive" title="b6">X</font>,<font color="Olive" title="b7">Y</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> ) </span> } </span>  holds <br/><font color="Olive" title="b3">F1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b4">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</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">  for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   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="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; <font color="Olive" title="b1">F1</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"><span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p3">(<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="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Olive" title="b2">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p3">(<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>,<font color="Olive" title="b3">P</font>)</span>)</span> where <font color="Olive" title="b3">P</font> is    <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> : ( <font color="Olive" title="b3">P</font> <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;  ex <font color="Olive" title="b4">X</font>, <font color="Olive" title="b5">Y</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="Olive" title="b3">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Olive" title="b4">X</font>,<font color="Olive" title="b5">Y</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> ) </span> } </span>  holds <br/><font color="Olive" title="b1">F1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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; <font color="Maroon" title="c4">F1</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"><span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p3">(<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="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c5">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p3">(<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>,<font color="Olive" title="b1">P</font>)</span>)</span> where <font color="Olive" title="b1">P</font> is    <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> : ( <font color="Olive" title="b1">P</font> <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;  ex <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">Y</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="Olive" title="b1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Olive" title="b2">X</font>,<font color="Olive" title="b3">Y</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> ) </span> } </span>  implies <font color="Maroon" title="c4">F1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">F2</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:82"/><span class="lab"><font color="Green" title="E61">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; <font color="Maroon" title="c4">F1</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"><span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p3">(<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="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c5">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p3">(<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>,<font color="Olive" title="b1">P</font>)</span>)</span> where <font color="Olive" title="b1">P</font> is    <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> : ( <font color="Olive" title="b1">P</font> <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;  ex <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">Y</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="Olive" title="b1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Olive" title="b2">X</font>,<font color="Olive" title="b3">Y</font>,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> ) </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="c4">F1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">F2</font></span><br/>

<span class="kw">assume </span><a NAME="E2:82"/>
<font color="Maroon" title="c4">F1</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c5">F2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:82"/><span class="kw">then </span>
<font color="Maroon" title="c4">F1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">F2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E5:82"/><span class="lab"><font color="Green" title="E62">A501</font></span>: 
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c5">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></span>;<br/>
<a NAME="E6:82"/><span class="lab"><font color="Green" title="E63">A50</font></span>: 
( <font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F1</font> &amp; <font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:82"><span class="lab"><font color="Green" title="E62">A501</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">P</font> being    <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"> such that </span><br/><a NAME="E8:82"/><span class="lab"><font color="Green" title="E64">A52</font></span>: 
( <font color="Maroon" title="c6">z</font> <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>,<font color="Maroon" title="c7">P</font>) &amp; <font color="Maroon" title="c7">P</font> <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;  ex <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</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="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</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="#E1:82"><span class="lab"><font color="Green" title="E61">AS</font></span></a>, <a class="txt" href="#E6:82"><span class="lab"><font color="Green" title="E63">A50</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">X1</font>, <font color="Maroon" title="c9">Y1</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="E10:82"/><span class="lab"><font color="Green" title="E65">A53</font></span>: 
<font color="Maroon" title="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c8">X1</font>,<font color="Maroon" title="c9">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="#E8:82"><span class="lab"><font color="Green" title="E64">A52</font></span></a></span>;<br/>
<a NAME="E11:82"/><span class="lab"><font color="Green" title="E66">A55</font></span>: 
<font color="Maroon" title="c6">z</font> <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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></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="#E1:82"><span class="lab"><font color="Green" title="E61">AS</font></span></a>, <a class="txt" href="#E6:82"><span class="lab"><font color="Green" title="E63">A50</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">Q</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></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="ec_pf_1.html#E56"><span class="lab"><font color="Green" title="E46">LML</font></span></a></span>;<br/>
<a NAME="E13:82"/><span class="lab"><font color="Green" title="E67">A57</font></span>: 
<font color="Maroon" title="c10">Q</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <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>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#T45" target="_self" title="EC_PF_1:th.45">ECZERO</a></span>;<br/>
<a NAME="E14:82"/>
<font color="Maroon" title="c10">Q</font> <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>,<font color="Maroon" title="c7">P</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:82"><span class="lab"><font color="Green" title="E64">A52</font></span></a>, <a class="txt" href="#E11:82"><span class="lab"><font color="Green" title="E66">A55</font></span></a>, <a class="ref" href="eqrel_1.html#T23" title="EQREL_1:th.23">EQREL_1:23</a></span>;<br/>
<a NAME="E15:82"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">P</font>,<font color="Maroon" title="c10">Q</font></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/>
<a NAME="E16:82"/><span class="kw">then </span>
<font color="Maroon" title="c7">P</font> <a href="ec_pf_1.html#R1" title="EC_PF_1:pred.1">_EQ_</a> <font color="Maroon" title="c10">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="#E1:82"><span class="lab"><font color="Green" title="E61">AS</font></span></a>, <a class="txt" href="#E13:82"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="txt" href="#E8:82"><span class="lab"><font color="Green" title="E64">A52</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">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="E18:82"/><span class="lab"><font color="Green" title="E68">P08</font></span>: 
( <font color="Maroon" title="c11">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="c10">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="c11">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> &amp; <font color="Maroon" title="c10">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="c11">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> &amp; <font color="Maroon" title="c10">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="c11">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">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="E19:82"/><span class="lab"><font color="Green" title="E69">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="E70">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="#E19:82"><span class="lab"><font color="Green" title="E69">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="c7">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="txt" href="#E10:82"><span class="lab"><font color="Green" title="E65">A53</font></span></a>, <a class="ref" href="mcart_1.html#T43" title="MCART_1:th.43">MCART_1:43</a></span>
;<br/>
 <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> = 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#T11" target="_self" title="EC_PF_1:th.11">XLm2</a></span>
<br/>.= 
<font color="Maroon" title="c11">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">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="#E18:82"><span class="lab"><font color="Green" title="E68">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="c11">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:82"><span class="lab"><font color="Green" title="E70">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">hence </span><a NAME="E22:82"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:82"><span class="lab"><font color="Green" title="E68">P08</font></span></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>
