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

<span class="kw">let </span><font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c2">x2</font>, <font color="Maroon" title="c3">x3</font>, <font color="Maroon" title="c4">x4</font>, <font color="Maroon" title="c5">x5</font>, <font color="Maroon" title="c6">x6</font>, <font color="Maroon" title="c7">x7</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c4">x4</font>,<font color="Maroon" title="c5">x5</font>,<font color="Maroon" title="c6">x6</font>,<font color="Maroon" title="c7">x7</font> <a href="zfmisc_1.html#R5" title="ZFMISC_1:pred.5">are_mutually_different</a>  implies <font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c5">x5</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c6">x6</font>,<font color="Maroon" title="c7">x7</font>,<font color="Maroon" title="c4">x4</font> <a href="zfmisc_1.html#R5" title="ZFMISC_1:pred.5">are_mutually_different</a>  )</span><br/>













<span class="kw">assume </span><a NAME="E1:11"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c4">x4</font>,<font color="Maroon" title="c5">x5</font>,<font color="Maroon" title="c6">x6</font>,<font color="Maroon" title="c7">x7</font> <a href="zfmisc_1.html#R5" title="ZFMISC_1:pred.5">are_mutually_different</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c5">x5</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c6">x6</font>,<font color="Maroon" title="c7">x7</font>,<font color="Maroon" title="c4">x4</font> <a href="zfmisc_1.html#R5" title="ZFMISC_1:pred.5">are_mutually_different</a> </span><br/>

<a NAME="E2:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A2</font></span>: 
<font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">x3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E3:11"/><span class="lab"><font color="Green" title="E6">A3</font></span>: 
<font color="Maroon" title="c5">x5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E4:11"/><span class="lab"><font color="Green" title="E7">A4</font></span>: 
<font color="Maroon" title="c5">x5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E5:11"/><span class="lab"><font color="Green" title="E8">A5</font></span>: 
<font color="Maroon" title="c4">x4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E6:11"/><span class="lab"><font color="Green" title="E9">A6</font></span>: 
<font color="Maroon" title="c4">x4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E7:11"/><span class="lab"><font color="Green" title="E10">A7</font></span>: 
<font color="Maroon" title="c6">x6</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E8:11"/><span class="lab"><font color="Green" title="E11">A8</font></span>: 
<font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E9:11"/><span class="lab"><font color="Green" title="E12">A9</font></span>: 
<font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E10:11"/><span class="lab"><font color="Green" title="E13">A10</font></span>: 
<font color="Maroon" title="c2">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E11:11"/><span class="lab"><font color="Green" title="E14">A11</font></span>: 
<font color="Maroon" title="c2">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">x3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E12:11"/><span class="lab"><font color="Green" title="E15">A12</font></span>: 
<font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E13:11"/><span class="lab"><font color="Green" title="E16">A13</font></span>: 
<font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E14:11"/><span class="lab"><font color="Green" title="E17">A14</font></span>: 
<font color="Maroon" title="c4">x4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E15:11"/><span class="lab"><font color="Green" title="E18">A15</font></span>: 
<font color="Maroon" title="c3">x3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E16:11"/><span class="lab"><font color="Green" title="E19">A16</font></span>: 
<font color="Maroon" title="c3">x3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E17:11"/><span class="lab"><font color="Green" title="E20">A17</font></span>: 
<font color="Maroon" title="c3">x3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E18:11"/><span class="lab"><font color="Green" title="E21">A18</font></span>: 
<font color="Maroon" title="c3">x3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E19:11"/><span class="lab"><font color="Green" title="E22">A19</font></span>: 
<font color="Maroon" title="c2">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">x7</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E20:11"/><span class="lab"><font color="Green" title="E23">A20</font></span>: 
<font color="Maroon" title="c2">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x6</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E21:11"/><span class="lab"><font color="Green" title="E24">A21</font></span>: 
<font color="Maroon" title="c2">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<a NAME="E22:11"/>
<font color="Maroon" title="c1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E23:11"/>
<font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c5">x5</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c6">x6</font>,<font color="Maroon" title="c7">x7</font>,<font color="Maroon" title="c4">x4</font> <a href="zfmisc_1.html#R5" title="ZFMISC_1:pred.5">are_mutually_different</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E9:11"><span class="lab"><font color="Green" title="E12">A9</font></span></a>, <a class="txt" href="#E8:11"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="txt" href="#E13:11"><span class="lab"><font color="Green" title="E16">A13</font></span></a>, <a class="txt" href="#E12:11"><span class="lab"><font color="Green" title="E15">A12</font></span></a>, <a class="txt" href="#E11:11"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E10:11"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="txt" href="#E21:11"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="txt" href="#E20:11"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="txt" href="#E19:11"><span class="lab"><font color="Green" title="E22">A19</font></span></a>, <a class="txt" href="#E18:11"><span class="lab"><font color="Green" title="E21">A18</font></span></a>, <a class="txt" href="#E17:11"><span class="lab"><font color="Green" title="E20">A17</font></span></a>, <a class="txt" href="#E16:11"><span class="lab"><font color="Green" title="E19">A16</font></span></a>, <a class="txt" href="#E15:11"><span class="lab"><font color="Green" title="E18">A15</font></span></a>, <a class="txt" href="#E14:11"><span class="lab"><font color="Green" title="E17">A14</font></span></a>, <a class="txt" href="#E6:11"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="txt" href="#E5:11"><span class="lab"><font color="Green" title="E8">A5</font></span></a>, <a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E7:11"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="ref" href="zfmisc_1.html#D9" title="ZFMISC_1:def.9">ZFMISC_1:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
