<?xml version="1.0"?>
<div class="add">

<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">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>  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">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; <font color="Olive" title="b3">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <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/> ex <font color="Olive" title="b4">Q</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> st <br/>( <font color="Olive" title="b4">Q</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; <font color="Olive" title="b4">Q</font> <a href="ec_pf_1.html#R1" title="EC_PF_1:pred.1">_EQ_</a> <font color="Olive" title="b3">P</font> &amp; <font color="Olive" title="b4">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> 1 )</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">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>  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">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; <font color="Olive" title="b1">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <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/> ex <font color="Olive" title="b2">Q</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> st <br/>( <font color="Olive" title="b2">Q</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; <font color="Olive" title="b2">Q</font> <a href="ec_pf_1.html#R1" title="EC_PF_1:pred.1">_EQ_</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b2">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> 1 )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">P</font> be    <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>; <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">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; <font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  ex <font color="Olive" title="b1">Q</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> st <br/>( <font color="Olive" title="b1">Q</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; <font color="Olive" title="b1">Q</font> <a href="ec_pf_1.html#R1" title="EC_PF_1:pred.1">_EQ_</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Olive" title="b1">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> 1 ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:77"/><span class="lab"><font color="Green" title="E56">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">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; <font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">Q</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> st <br/>( <font color="Olive" title="b1">Q</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; <font color="Olive" title="b1">Q</font> <a href="ec_pf_1.html#R1" title="EC_PF_1:pred.1">_EQ_</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Olive" title="b1">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> 1 )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">d</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> ;<br/>
<a NAME="E2:77"/><span class="lab"><font color="Green" title="E57">AS0</font></span>: 
<font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:77"><span class="lab"><font color="Green" title="E56">AS</font></span></a>, <a class="ref" href="ec_pf_1.html#T11" target="_self" title="EC_PF_1:th.11">XLm2</a></span>;<br/>
<a NAME="E3:77"/><span class="lab"><font color="Green" title="E58">AS1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:77_1"/><span class="lab"><font color="Green" title="E59">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="lab"><font color="Green" title="E60">A2</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> = 
 <a href="group_1.html#K1" title="GROUP_1:func.1">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:77"><span class="lab"><font color="Green" title="E57">AS0</font></span></a>, <a class="ref" href="vectsp_1.html#D10" title="VECTSP_1:def.10">VECTSP_1:def 10</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#T12" target="_self" title="EC_PF_1:th.12">XLm3</a></span>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> = 
 <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:77_1"><span class="lab"><font color="Green" title="E59">A1</font></span></a>, <a class="ref" href="vectsp_1.html#T12" title="VECTSP_1:th.12">VECTSP_1:12</a></span>
<br/>.= 
 <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/>
<span class="kw">hence </span><a NAME="E4:77_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:77_1"><span class="lab"><font color="Green" title="E60">A2</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><span class="kw">end;</span></div>
<span class="kw">reconsider </span><font color="Maroon" title="c6">Q</font> = <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> ;<br/>
<a NAME="E5:77"/><span class="lab"><font color="Green" title="E59">P1</font></span>: 
( <font color="Maroon" title="c6">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> &amp; <font color="Maroon" title="c6">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> &amp; <font color="Maroon" title="c6">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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="mcart_1.html#T43" title="MCART_1:th.43">MCART_1:43</a></span>;<br/>
<a NAME="E6:77"/><span class="kw">then </span>
<font color="Maroon" title="c6">Q</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>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:77"><span class="lab"><font color="Green" title="E56">AS</font></span></a>, <a class="txt" href="#E3:77"><span class="lab"><font color="Green" title="E58">AS1</font></span></a>, <a class="ref" href="ec_pf_1.html#T48" target="_self" title="EC_PF_1:th.48">LmEQV4</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">PP</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="E8:77"/><span class="lab"><font color="Green" title="E60">P2</font></span>: 
( <font color="Maroon" title="c6">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">PP</font> &amp; <span class="p1">(<span class="default"><a href="ec_pf_1.html#K5" title="EC_PF_1:func.5">EC_WEqProjCo</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">p</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">PP</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> )
 ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">Q</font> = <font color="Maroon" title="c6">Q</font> 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="#E8:77"><span class="lab"><font color="Green" title="E60">P2</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">Q</font>
; <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="c8">Q</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; <font color="Maroon" title="c8">Q</font> <a href="ec_pf_1.html#R1" title="EC_PF_1:pred.1">_EQ_</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c8">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> 1 )</span><br/>

<span class="kw">thus </span><a NAME="E10:77"/>
<font color="Maroon" title="c8">Q</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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:77"><span class="lab"><font color="Green" title="E59">P1</font></span></a>, <a class="txt" href="#E1:77"><span class="lab"><font color="Green" title="E56">AS</font></span></a>, <a class="txt" href="#E3:77"><span class="lab"><font color="Green" title="E58">AS1</font></span></a>, <a class="ref" href="ec_pf_1.html#T48" target="_self" title="EC_PF_1:th.48">LmEQV4</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="c8">Q</font> <a href="ec_pf_1.html#R1" title="EC_PF_1:pred.1">_EQ_</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c8">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> 1 )</span><br/>

<span class="kw">thus </span><a NAME="E11:77"/>
<font color="Maroon" title="c8">Q</font> <a href="ec_pf_1.html#R1" title="EC_PF_1:pred.1">_EQ_</a> <font color="Maroon" title="c4">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:77"><span class="lab"><font color="Green" title="E59">P1</font></span></a>, <a class="txt" href="#E3:77"><span class="lab"><font color="Green" title="E58">AS1</font></span></a>, <a class="ref" href="ec_pf_1.html#D10" target="_self" title="EC_PF_1:def.10">DefEQV</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="c8">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> 1</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c8">Q</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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="mcart_1.html#D7" title="MCART_1:def.7">MCART_1:def 7</a></span>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:77"><span class="lab"><font color="Green" title="E57">AS0</font></span></a>, <a class="ref" href="vectsp_1.html#D10" title="VECTSP_1:def.10">VECTSP_1:def 10</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_1.html#T12" target="_self" title="EC_PF_1:th.12">XLm3</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>
