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

<b>let </b><font color="Maroon" title="c1">Y</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> ;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ;<br/>



<b>assume </b><a NAME="E1:3"/><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font>
 ;<br/>

<a NAME="E2:3"/>
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>;<br/>

<a NAME="E1:3_1"/>
<font color="Maroon" title="c2">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<b>by </b><i><a class="txt" href="bvfunc_5.html#E1:3"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="bvfunc_1.html#D14" title="BVFUNC_1:def.14">BVFUNC_1:def 14</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> = 
<a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#D7" title="BVFUNC_1:def.7">BVFUNC_1:def 7</a></i>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
<b>by </b><i><a class="ref" href="binarith.html#T19" title="BINARITH:th.19">BINARITH:19</a></i>
;<br/>
<b>hence </b><a NAME="E3:3_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:3"/>
<font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K6" title="BVFUNC_1:func.6">'or'</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="ref" href="bvfunc_1.html#D14" title="BVFUNC_1:def.14">BVFUNC_1:def 14</a></i>;<br/>


</div>
