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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">T</font> being <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a> <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font><br/> for <font color="Olive" title="b2">b1</font>, <font color="Olive" title="b3">b2</font>, <font color="Olive" title="b4">b3</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b2">b1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Olive" title="b3">b2</font>,<font color="Olive" title="b1">T</font> holds <br/><font color="Olive" title="b2">b1</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Olive" title="b4">b3</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Olive" title="b3">b2</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Olive" title="b4">b3</font>,<font color="Olive" title="b1">T</font></span><br/><b>let </b><font color="Maroon" title="c2">T</font> be  <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a> <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b1</font>, <font color="Olive" title="b2">b2</font>, <font color="Olive" title="b3">b3</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">b1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Olive" title="b2">b2</font>,<font color="Maroon" title="c2">T</font> holds <br/><font color="Olive" title="b1">b1</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Olive" title="b3">b3</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Olive" title="b2">b2</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Olive" title="b3">b3</font>,<font color="Maroon" title="c2">T</font></span><br/><b>let </b><font color="Maroon" title="c3">b1</font>, <font color="Maroon" title="c4">b2</font>, <font color="Maroon" title="c5">b3</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">b1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font> implies <font color="Maroon" title="c3">b1</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Maroon" title="c5">b3</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Maroon" title="c5">b3</font>,<font color="Maroon" title="c2">T</font> )</span><br/>





<b>assume </b><a NAME="E1:2"/>
<font color="Maroon" title="c3">b1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font>,<font color="Maroon" title="c2">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">b1</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Maroon" title="c5">b3</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Maroon" title="c5">b3</font>,<font color="Maroon" title="c2">T</font></span><br/>

<a NAME="E2:2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="ref" href="termord.html#D2" title="TERMORD:def.2">TERMORD:def 2</a></i>;<br/>
<a NAME="E3:2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Maroon" title="c5">b3</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">b2</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Maroon" title="c5">b3</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="ref" href="bagorder.html#D7" title="BAGORDER:def.7">BAGORDER:def 7</a></i>;<br/>
<b>hence </b><a NAME="E4:2"/>
<font color="Maroon" title="c3">b1</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Maroon" title="c5">b3</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c4">b2</font> <a href="polynom1.html#K7" title="POLYNOM1:func.7">+</a> <font color="Maroon" title="c5">b3</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="termord.html#D2" title="TERMORD:def.2">TERMORD:def 2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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