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<span class="kw">let </span><font color="Maroon" title="c4">IT1</font>, <font color="Maroon" title="c5">IT2</font> be   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">IT1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">B</font> &amp; (  for <font color="Olive" title="b1">x</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">B</font> holds <br/><font color="Olive" title="b1">x</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">IT1</font>,<font color="Maroon" title="c2">T</font> ) &amp; <font color="Maroon" title="c5">IT2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">B</font> &amp; (  for <font color="Olive" title="b1">x</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">B</font> holds <br/><font color="Olive" title="b1">x</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c5">IT2</font>,<font color="Maroon" title="c2">T</font> ) implies <font color="Maroon" title="c4">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">IT2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:17_1_2"/><span class="lab"><font color="Green" title="E12">A32</font></span>: 
<font color="Maroon" title="c4">IT1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">and </span><br/><a NAME="E2:17_1_2"/><span class="lab"><font color="Green" title="E13">A33</font></span>: 
 for <font color="Olive" title="b1">x</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">B</font> holds <br/><font color="Olive" title="b1">x</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">IT1</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">and </span><br/><a NAME="E3:17_1_2"/><span class="lab"><font color="Green" title="E14">A34</font></span>: 
<font color="Maroon" title="c5">IT2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">and </span><br/><a NAME="E4:17_1_2"/><span class="lab"><font color="Green" title="E15">A35</font></span>: 
 for <font color="Olive" title="b1">x</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">B</font> holds <br/><font color="Olive" title="b1">x</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c5">IT2</font>,<font color="Maroon" title="c2">T</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">IT2</font></span><br/>

<a NAME="E5:17_1_2"/><span class="lab"><font color="Green" title="E16">A36</font></span>: 
<font color="Maroon" title="c4">IT1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c5">IT2</font>,<font color="Maroon" title="c2">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17_1_2"><span class="lab"><font color="Green" title="E12">A32</font></span></a>, <a class="txt" href="#E4:17_1_2"><span class="lab"><font color="Green" title="E15">A35</font></span></a></span>;<br/>
<a NAME="E6:17_1_2"/>
<font color="Maroon" title="c5">IT2</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">IT1</font>,<font color="Maroon" title="c2">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17_1_2"><span class="lab"><font color="Green" title="E13">A33</font></span></a>, <a class="txt" href="#E3:17_1_2"><span class="lab"><font color="Green" title="E14">A34</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:17_1_2"/>
<font color="Maroon" title="c4">IT1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">IT2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17_1_2"><span class="lab"><font color="Green" title="E16">A36</font></span></a>, <a class="ref" href="termord.html#T7" onmouseover="rs('termord/T7')" onmouseout="rh()">TERMORD:7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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