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<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="c7">x7</font>,<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> <a href="zfmisc_1.html#R5" title="ZFMISC_1:pred.5">are_mutually_different</a>  )</span><br/>













<span class="kw">assume </span><a NAME="E1:10"/><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="c7">x7</font>,<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> <a href="zfmisc_1.html#R5" title="ZFMISC_1:pred.5">are_mutually_different</a> </span><br/>

<a NAME="E2:10"/><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="E3:10"/><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="#E1:10"><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="E4:10"/><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="#E1:10"><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="E5:10"/><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="#E1:10"><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="E6:10"/><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="#E1:10"><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="E7:10"/><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="#E1:10"><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="E8:10"/><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="#E1:10"><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="E9:10"/><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="#E1:10"><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="E10:10"/><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="#E1:10"><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="E11:10"/><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="#E1:10"><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="E12:10"/><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="#E1:10"><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="E13:10"/><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="#E1:10"><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="E14:10"/><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="#E1:10"><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="E15:10"/><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="#E1:10"><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="E16:10"/><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="#E1:10"><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="E17:10"/><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="#E1:10"><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="E18:10"/><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="#E1:10"><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="E19:10"/><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="#E1:10"><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="E20:10"/><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="#E1:10"><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="E21:10"/><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="#E1:10"><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="E22:10"/>
<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="#E1:10"><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="E23:10"/>
<font color="Maroon" title="c7">x7</font>,<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> <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="#E2:10"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E9:10"><span class="lab"><font color="Green" title="E12">A9</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E16">A13</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E15">A12</font></span></a>, <a class="txt" href="#E11:10"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="txt" href="#E21:10"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="txt" href="#E20:10"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="txt" href="#E19:10"><span class="lab"><font color="Green" title="E22">A19</font></span></a>, <a class="txt" href="#E18:10"><span class="lab"><font color="Green" title="E21">A18</font></span></a>, <a class="txt" href="#E17:10"><span class="lab"><font color="Green" title="E20">A17</font></span></a>, <a class="txt" href="#E16:10"><span class="lab"><font color="Green" title="E19">A16</font></span></a>, <a class="txt" href="#E15:10"><span class="lab"><font color="Green" title="E18">A15</font></span></a>, <a class="txt" href="#E14:10"><span class="lab"><font color="Green" title="E17">A14</font></span></a>, <a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E8">A5</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E7:10"><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/>


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