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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="margrel1.html#V2">boolean</a>  <a href="hidden.html#M1">set</a> ;<br/>



<a NAME="E1:21"/><i><font color="Green">E3</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K2">'eqv'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  implies ( <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K2">'eqv'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/>

<a NAME="E2:21_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 
<b>by </b><i><a class="ref" href="binari_5.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E3:21_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 <b>by </b><i><a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:21"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  implies <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K2">'eqv'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 ;<br/>

<a NAME="E2:21_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 
<b>by </b><i><a class="ref" href="margrel1.html#D17">MARGREL1:def 17</a></i>;<br/>
<b>hence </b><a NAME="E3:21_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K2">'eqv'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="ref" href="binari_5.html#T23" target="_self">Th23</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:21"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K2">'eqv'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  iff ( <font color="Maroon">c<sub>1</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="bvfunc_1.html#K1">'imp'</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) )
 <b>by </b><i><a class="txt" href="binari_5.html#E1:21"><i><font color="Green">E3</font></i></a></i>;<br/>


</div>
