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

<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="c0sp1.html#K7" title="C0SP1:func.7">R_Algebra_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> 1</span><br/>

<a NAME="E1:40"/><i><font color="Green" title="E28">A1</font></i>: 
 <a href="c0sp1.html#K7" title="C0SP1:func.7">R_Algebra_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font> is    <a href="c0sp1.html#M2" title="C0SP1:mode.2">Subalgebra</a> of  <a href="funcsdom.html#K12" title="FUNCSDOM:func.12">RAlgebra</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="c0sp1.html#T6" target="_self" title="C0SP1:th.6">Th03</a></i>;<br/>
<a NAME="E2:40"/>
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="funcsdom.html#K12" title="FUNCSDOM:func.12">RAlgebra</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> 1
 
;<br/>
<b>hence </b><a NAME="E3:40"/>
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="c0sp1.html#K7" title="C0SP1:func.7">R_Algebra_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> 1
 <b>by </b><i><a class="txt" href="#E1:40"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="c0sp1.html#T8" target="_self" title="C0SP1:th.8">RLSUB121</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
