<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon" title="c1">G</font> =  <a href="vectsp_1.html#K1" title="VECTSP_1:func.1">G_Real</a> ;<br/>
<b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K1" title="VECTSP_1:func.1">G_Real</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K1" title="VECTSP_1:func.1">G_Real</a>  st <font color="Olive" title="b1">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c4">b'</font> = <font color="Maroon" title="c3">a</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2 as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<b>consider </b><font color="Maroon" title="c5">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K1" title="VECTSP_1:func.1">G_Real</a> <b> such that </b><br/><a NAME="E4:1"/><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b'</font>
 ;<br/>
<a NAME="E5:1"/>
<font color="Maroon" title="c5">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="#E4:1"><i><font color="Green" title="E2">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:1"/>
 ex <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K1" title="VECTSP_1:func.1">G_Real</a>  st <font color="Olive" title="b1">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
