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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be    <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>;<br/>





<a NAME="E1:14"/><i><font color="Green" title="E10">A1</font></i>: 
( 1 <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; 1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x1</font> &amp; 0 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">x1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x1</font> )
 
<b>by </b><i><a class="ref" href="euclid_4.html#T1" target="_self" title="EUCLID_4:th.1">Th1</a>, <a class="ref" href="euclid_4.html#T3" target="_self" title="EUCLID_4:th.3">Th3</a></i>;<br/>
<a NAME="E2:14"/>
( 1 <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; 0 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font> &amp; 1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> &amp; <span class="p1">(<span class="default"><a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> )
 
<b>by </b><i><a class="ref" href="euclid_4.html#T1" target="_self" title="EUCLID_4:th.1">Th1</a>, <a class="ref" href="euclid_4.html#T3" target="_self" title="EUCLID_4:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E3:14"/>
( <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font> &amp; <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclid_4.html#K2" title="EUCLID_4:func.2">Line</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font> )
 <b>by </b><i><a class="txt" href="euclid_4.html#E1:14"><i><font color="Green" title="E10">A1</font></i></a></i>;<br/>


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