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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> 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>  ex <font color="Olive" title="b2">n1</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">n1</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c1">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</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">  ex <font color="Olive" title="b1">n1</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">n1</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c1">p</font></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">a</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> <font color="Maroon" title="c1">p</font> ;<br/>
<a NAME="E2:24"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">p</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algseq_1.html#T1" title="ALGSEQ_1:th.1">ALGSEQ_1:1</a></span>;<br/>
<a NAME="E3:24"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c1">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T63" title="NAT_D:th.63">NAT_D:63</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:24"/>
 ex <font color="Olive" title="b1">n1</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">n1</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c1">p</font>
 ; <a class="txt" 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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