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<b>let </b><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">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> 3</span>)</span>;<br/>



<b>reconsider </b><font color="Maroon" title="c3">p1'</font> = <font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c4">p2'</font> = <font color="Maroon" title="c2">p2</font> as    <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> 3 <b>by </b><i><a class="ref" href="euclid.html#T25" title="EUCLID:th.25">EUCLID:25</a></i>;<br/>
<a NAME="E2:7"/>
<font color="Maroon" title="c1">p1</font> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <font color="Maroon" title="c2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p1'</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c4">p2'</font>
 
;<br/>
<a NAME="E3:7"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p1'</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c4">p2'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<b>by </b><i><a class="ref" href="euclid.html#T28" title="EUCLID:th.28">EUCLID:28</a></i>;<br/>
<a NAME="E4:7"/><b>then </b><i><font color="Green" title="E5">A1</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p1'</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c4">p2'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:7"/><b>then </b><i><font color="Green" title="E6">A2</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p1'</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c4">p2'</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E6:7"/><i><font color="Green" title="E7">A3</font></i>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p1'</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c4">p2'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="euclid_5.html#E4:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E7:7"/><i><font color="Green" title="E8">A4</font></i>: 
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p1'</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c4">p2'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="euclid_5.html#E4:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E8:7"/><i><font color="Green" title="E9">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="euclid_5.html#E5:7"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="valued_1.html#D1" title="VALUED_1:def.1">VALUED_1:def 1</a></i>;<br/>
<a NAME="E9:7"/><i><font color="Green" title="E10">A6</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="euclid_5.html#E6:7"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="valued_1.html#D1" title="VALUED_1:def.1">VALUED_1:def 1</a></i>;<br/>
<a NAME="E10:7"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="euclid_5.html#E7:7"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="valued_1.html#D1" title="VALUED_1:def.1">VALUED_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:7"/>
<font color="Maroon" title="c1">p1</font> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <font color="Maroon" title="c2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span>
 <b>by </b><i><a class="txt" href="euclid_5.html#E8:7"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="euclid_5.html#E9:7"><i><font color="Green" title="E10">A6</font></i></a>, <a class="ref" href="euclid_5.html#T3" target="_self" title="EUCLID_5:th.3">Th3</a></i>;<br/>


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