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<div><span class="kw">theorem </span><a NAME="T33"><span class="comment"><font color="firebrick">:: EC_PF_2:33</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>, <font color="Olive" title="b4">Px</font>, <font color="Olive" title="b5">Py</font>, <font color="Olive" title="b6">Pz</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="b7">P</font> being    <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="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b1">p</font>)  st <font color="Olive" title="b7">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">Px</font>,<font color="Olive" title="b5">Py</font>,<font color="Olive" title="b6">Pz</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> holds <br/>( <font color="Olive" title="b7">P</font> <a href="ec_pf_2.html#K4" title="EC_PF_2:func.4">`1_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">Px</font> &amp; <font color="Olive" title="b7">P</font> <a href="ec_pf_2.html#K5" title="EC_PF_2:func.5">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">Py</font> &amp; <font color="Olive" title="b7">P</font> <a href="ec_pf_2.html#K6" title="EC_PF_2:func.6">`3_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">Pz</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="ec_pf_2.html#D3" target="_self" onmouseover="rs('ec_pf_2/D3')" onmouseout="rh()">Def3</a>, <a class="ref" href="ec_pf_2.html#D4" target="_self" onmouseover="rs('ec_pf_2/D4')" onmouseout="rh()">Def4</a>, <a class="ref" href="ec_pf_2.html#D5" target="_self" onmouseover="rs('ec_pf_2/D5')" onmouseout="rh()">Def5</a></span>;<br/></div></div>
