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<span class="kw">let </span><font color="Maroon" title="c4">z1</font>, <font color="Maroon" title="c5">z2</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"> ( ( for <font color="Olive" title="b1">y1</font>, <font color="Olive" title="b2">y2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">y1</font>,<font color="Olive" title="b2">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/><font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y1</font> ) &amp; ( for <font color="Olive" title="b1">y1</font>, <font color="Olive" title="b2">y2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">y1</font>,<font color="Olive" title="b2">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/><font color="Maroon" title="c5">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y1</font> ) implies <font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">z2</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:7_1_2"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
for <font color="Olive" title="b1">y1</font>, <font color="Olive" title="b2">y2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">y1</font>,<font color="Olive" title="b2">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/><font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y1</font>
 <span class="kw">and </span><br/><a NAME="E2:7_1_2"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
for <font color="Olive" title="b1">y1</font>, <font color="Olive" title="b2">y2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">y1</font>,<font color="Olive" title="b2">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/><font color="Maroon" title="c5">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y1</font>
 ; <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="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">z2</font></span><br/>

<a NAME="E3:7_1_2"/>
<font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="txt" href="#E1:7_1_2"><span class="lab"><font color="Green" title="E6">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:7_1_2"/>
<font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">z2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="txt" href="#E2:7_1_2"><span class="lab"><font color="Green" title="E7">A3</font></span></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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