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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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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> holds  <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> 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="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c1">p</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> 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><br/>





<a NAME="E1:56"/>
( <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> 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> &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_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></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="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="ec_pf_1.html#E55"><span class="lab"><font color="Green" title="E42">Lm5</font></span></a></span>;<br/>
<a NAME="E2:56"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">P</font> 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> : <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="Olive" title="b1">P</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> </span> } </span> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:56"/>
<span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> 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>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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