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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span> holds   <a href="euclid_4.html#K3" title="EUCLID_4:func.3">Line</a> <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K3" title="EUCLID_4:func.3">Line</a> <font color="Olive" title="b2">p2</font>,<font color="Olive" title="b1">p1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p1</font>, <font color="Maroon" title="c3">p2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="euclid_4.html#K3" title="EUCLID_4:func.3">Line</a> <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K3" title="EUCLID_4:func.3">Line</a> <font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p1</font></span><br/>





<a NAME="E1:50"/>
(  ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font> st <br/>( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p1</font> &amp; <font color="Olive" title="b2">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p2</font> &amp;  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> <font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K3" title="EUCLID_4:func.3">Line</a> <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font> ) &amp;  ex <font color="Olive" title="b1">x29</font>, <font color="Olive" title="b2">x19</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font> st <br/>( <font color="Olive" title="b1">x29</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p2</font> &amp; <font color="Olive" title="b2">x19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p1</font> &amp;  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> <font color="Olive" title="b1">x29</font>,<font color="Olive" title="b2">x19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K3" title="EUCLID_4:func.3">Line</a> <font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p1</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="euclid_4.html#E60"><span class="lab"><font color="Green" title="E28">Lm8</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:50"/>
 <a href="euclid_4.html#K3" title="EUCLID_4:func.3">Line</a> <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_4.html#K3" title="EUCLID_4:func.3">Line</a> <font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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