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

<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#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> &amp; <font color="Olive" title="b3">b2</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <font color="Olive" title="b4">b3</font>,<font color="Olive" title="b1">T</font> holds <br/><font color="Olive" title="b2">b1</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</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#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> &amp; <font color="Olive" title="b2">b2</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <font color="Olive" title="b3">b3</font>,<font color="Maroon" title="c2">T</font> holds <br/><font color="Olive" title="b1">b1</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</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> &amp; <font color="Maroon" title="c4">b2</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <font color="Maroon" title="c5">b3</font>,<font color="Maroon" title="c2">T</font> implies <font color="Maroon" title="c3">b1</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <font color="Maroon" title="c5">b3</font>,<font color="Maroon" title="c2">T</font> )</span><br/>





<b>assume </b><a NAME="E1:3"/><i><font color="Green" title="E4">A1</font></i>: 
( <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> &amp; <font color="Maroon" title="c4">b2</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <font color="Maroon" title="c5">b3</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="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <font color="Maroon" title="c5">b3</font>,<font color="Maroon" title="c2">T</font></span><br/>

<a NAME="E2:3"/><b>then </b><i><font color="Green" title="E5">A2</font></i>: 
( <font color="Maroon" title="c4">b2</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c5">b3</font>,<font color="Maroon" title="c2">T</font> &amp; <font color="Maroon" title="c4">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b3</font> )
 
<b>by </b><i><a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></i>;<br/>
<a NAME="E3:3"/><b>then </b><i><font color="Green" title="E6">A3</font></i>: 
<font color="Maroon" title="c3">b1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c5">b3</font>,<font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:3"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="termord.html#T8" title="TERMORD:th.8">TERMORD:8</a></i>;<br/>
<a NAME="E4:3"/>
<font color="Maroon" title="c3">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b3</font>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:3"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="groeb_3.html#E2:3"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="termord.html#T7" title="TERMORD:th.7">TERMORD:7</a></i>;<br/>
<b>hence </b><a NAME="E5:3"/>
<font color="Maroon" title="c3">b1</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <font color="Maroon" title="c5">b3</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E3:3"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
