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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E52">Th49</font></span>: <a NAME="T49"><span class="comment"><font color="firebrick">:: EC_PF_1:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font> being   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">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="Olive" title="b1">p</font></span>)</span><br/>  for <font color="Olive" title="b4">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="Olive" title="b1">p</font></span>)</span>  st <font color="Olive" title="b1">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="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b1">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="Olive" title="b1">p</font></span>)</span> &amp; <font color="Olive" title="b4">P</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ec_pf_1.html#K6" title="EC_PF_1:func.6">EC_SetProjCo</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b1">p</font>) &amp; <font color="Olive" title="b4">P</font> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> ex <font color="Olive" title="b5">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="Olive" title="b1">p</font></span>)</span> st <br/>( <font color="Olive" title="b5">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ec_pf_1.html#K6" title="EC_PF_1:func.6">EC_SetProjCo</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b1">p</font>) &amp; <font color="Olive" title="b5">Q</font> <a href="ec_pf_1.html#R1" title="EC_PF_1:pred.1">_EQ_</a> <font color="Olive" title="b4">P</font> &amp; <font color="Olive" title="b5">Q</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">Q</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b5">Q</font> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</div></div>
