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<b>let </b><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon" title="c3">p1</font>, <font color="Maroon" title="c4">p2</font>, <font color="Maroon" title="c5">p3</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> 2</span>)</span>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:41"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c2">f</font> is <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>
 <b>and </b><br/><a NAME="E2:41"/><i><font color="Green" title="E30">A2</font></i>: 
<font color="Maroon" title="c2">f</font> is <a href="sppol_1.html#V3" title="SPPOL_1:attr.3">alternating</a>
 <b>and </b><br/><a NAME="E3:41"/><i><font color="Green" title="E31">A3</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font>
 <b>and </b><br/><a NAME="E4:41"/><i><font color="Green" title="E32">A4</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font>
 <b>and </b><br/><a NAME="E5:41"/><i><font color="Green" title="E33">A5</font></i>: 
<font color="Maroon" title="c3">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">i</font>
 <b>and </b><br/><a NAME="E6:41"/><i><font color="Green" title="E34">A6</font></i>: 
<font color="Maroon" title="c4">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>and </b><br/><a NAME="E7:41"/><i><font color="Green" title="E35">A7</font></i>: 
<font color="Maroon" title="c5">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
 ;<br/>

<a NAME="E8:41"/>
<font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E9:41"/><b>then </b>
<font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font>
 
<b>by </b><i><a class="txt" href="sppol_1.html#E4:41"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E10:41"/><b>then </b>
( <font color="Maroon" title="c3">p1</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p2</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  or <font color="Maroon" title="c3">p1</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p2</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  )
 
<b>by </b><i><a class="txt" href="sppol_1.html#E1:41"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="sppol_1.html#E3:41"><i><font color="Green" title="E31">A3</font></i></a>, <a class="txt" href="sppol_1.html#E5:41"><i><font color="Green" title="E33">A5</font></i></a>, <a class="txt" href="sppol_1.html#E6:41"><i><font color="Green" title="E34">A6</font></i></a>, <a class="ref" href="topreal1.html#D7" title="TOPREAL1:def.7">TOPREAL1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E11:41"/>
( ( <font color="Maroon" title="c3">p1</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p2</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  &amp; <font color="Maroon" title="c5">p3</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">p2</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  ) or ( <font color="Maroon" title="c3">p1</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p2</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  &amp; <font color="Maroon" title="c5">p3</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">p2</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  ) )
 <b>by </b><i><a class="txt" href="sppol_1.html#E2:41"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="sppol_1.html#E3:41"><i><font color="Green" title="E31">A3</font></i></a>, <a class="txt" href="sppol_1.html#E4:41"><i><font color="Green" title="E32">A4</font></i></a>, <a class="txt" href="sppol_1.html#E5:41"><i><font color="Green" title="E33">A5</font></i></a>, <a class="txt" href="sppol_1.html#E7:41"><i><font color="Green" title="E35">A7</font></i></a>, <a class="ref" href="sppol_1.html#D4" target="_self" title="SPPOL_1:def.4">Def4</a></i>;<br/>


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