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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>; <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">  <a href="bagorder.html#NK4" title="BAGORDER:NK.4">LexOrder</a> <font color="Maroon" title="c1">n</font> is  <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="33_1"><span class="kw">now </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">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font> &amp;  not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <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="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font> &amp;  not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:33_1"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">and </span><br/><a NAME="E2:33_1"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c4">a9</font> = <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c5">b9</font> = <font color="Maroon" title="c3">b</font> as   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E2:33_1"><span class="lab"><font color="Green" title="E20">A2</font></span></a></span>;<br/><a NAME="E4:33_1"/>
( <font color="Maroon" title="c4">a9</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c5">b9</font> or <font color="Maroon" title="c5">b9</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c4">a9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T45" onmouseover="rs('pre_poly/T45')" onmouseout="rh()">PRE_POLY:45</a></span>;<br/><span class="kw">hence </span><a NAME="E5:33_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D14" onmouseover="rs('pre_poly/D14')" onmouseout="rh()">PRE_POLY:def 14</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:33"/>
 <a href="bagorder.html#NK4" title="BAGORDER:NK.4">LexOrder</a> <font color="Maroon" title="c1">n</font> <a href="relat_2.html#R7" title="RELAT_2:pred.7">is_strongly_connected_in</a>  <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="bagorder.html#D5" target="_self" onmouseover="rs('bagorder/D5')" onmouseout="rh()">BAGORDER:def 5</a> <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"> ( (  for <font color="Olive" title="b1">a</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> holds  <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Olive" title="b1">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bagorder.html#NK4" title="BAGORDER:NK.4">LexOrder</a> <font color="Maroon" title="c1">n</font> ) &amp; (  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bagorder.html#NK4" title="BAGORDER:NK.4">LexOrder</a> <font color="Maroon" title="c1">n</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b3">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b3">c</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>  <a href="bagorder.html#NK4" title="BAGORDER:NK.4">LexOrder</a> <font color="Maroon" title="c1">n</font> ) )</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="33_2"><span class="kw">now </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">  for <font color="Olive" title="b1">a</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> holds  <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Olive" title="b1">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">a</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"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font></span><br/><a NAME="E1:33_2"/>
 <a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T60" onmouseover="rs('pre_poly/T60')" onmouseout="rh()">PRE_POLY:60</a></span>;<br/><span class="kw">hence </span><a NAME="E2:33_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D14" onmouseover="rs('pre_poly/D14')" onmouseout="rh()">PRE_POLY:def 14</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:33"/>
 for <font color="Olive" title="b1">a</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> holds  <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Olive" title="b1">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bagorder.html#NK4" title="BAGORDER:NK.4">LexOrder</a> <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">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bagorder.html#NK4" title="BAGORDER:NK.4">LexOrder</a> <font color="Maroon" title="c1">n</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b3">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b3">c</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>  <a href="bagorder.html#NK4" title="BAGORDER:NK.4">LexOrder</a> <font color="Maroon" title="c1">n</font></span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="33_3"><span class="kw">now </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">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b3">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b3">c</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>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> implies <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="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</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>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font> )</span><br/><span class="kw">assume </span><a NAME="E1:33_3"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <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"> <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="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</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>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font></span><br/><a NAME="E2:33_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D14" onmouseover="rs('pre_poly/D14')" onmouseout="rh()">PRE_POLY:def 14</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="33_3_1"><span class="kw">now </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"> <font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_3_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:33_3_1_1"/>
( <font color="Maroon" title="c2">a</font> <a href="pre_poly.html#R1" title="PRE_POLY:pred.1">&lt;</a> <font color="Maroon" title="c3">b</font> or <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33_3"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="pre_poly.html#D10" onmouseover="rs('pre_poly/D10')" onmouseout="rh()">PRE_POLY:def 10</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_3_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:33_3_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="pre_poly.html#R1" title="PRE_POLY:pred.1">&lt;</a> <font color="Maroon" title="c3">b</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="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">k</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><span class="kw"> such that </span><br/><a NAME="E3:33_3_1_1_1"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c5">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">b</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c5">k</font>
 <span class="kw">and </span><br/><a NAME="E4:33_3_1_1_1"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
 for <font color="Olive" title="b1">l</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st <font color="Olive" title="b1">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">k</font> holds <br/><font color="Maroon" title="c2">a</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D9" onmouseover="rs('pre_poly/D9')" onmouseout="rh()">PRE_POLY:def 9</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="33_3_1_1_1_1"><span class="kw">now </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">  ex <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">k</font> &amp; (  for <font color="Olive" title="b2">l</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st <font color="Olive" title="b2">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">k</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">l</font> ) )</span></a><div class="add"><span class="kw">take </span><font color="Maroon" title="c6">k</font> = <font color="Maroon" title="c5">k</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"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">k</font> &amp; (  for <font color="Olive" title="b1">l</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st <font color="Olive" title="b1">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">k</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">l</font> ) )</span><br/><a NAME="E1:33_3_1_1_1_1"/><span class="lab"><font color="Green" title="E22">A6</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D5" onmouseover="rs('pre_poly/D5')" onmouseout="rh()">PRE_POLY:def 5</a></span>;<br/><a NAME="E2:33_3_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D5" onmouseover="rs('pre_poly/D5')" onmouseout="rh()">PRE_POLY:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:33_3_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33_3_1_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E1:33_3_1_1_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</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">  for <font color="Olive" title="b1">l</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st <font color="Olive" title="b1">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">k</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">l</font> be   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>; <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="c7">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">k</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font> )</span><br/><span class="kw">assume </span><a NAME="E4:33_3_1_1_1_1"/><span class="lab"><font color="Green" title="E23">A7</font></span>: 
<font color="Maroon" title="c7">l</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">k</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font></span><br/><a NAME="E5:33_3_1_1_1_1"/><span class="lab"><font color="Green" title="E24">A8</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D5" onmouseover="rs('pre_poly/D5')" onmouseout="rh()">PRE_POLY:def 5</a></span>;<br/><a NAME="E6:33_3_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D5" onmouseover="rs('pre_poly/D5')" onmouseout="rh()">PRE_POLY:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E7:33_3_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:33_3_1_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E4:33_3_1_1_1_1"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E5:33_3_1_1_1_1"><span class="lab"><font color="Green" title="E24">A8</font></span></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/></div><span class="kw">end;</span></div><a NAME="E6:33_3_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font> <a href="pre_poly.html#R1" title="PRE_POLY:pred.1">&lt;</a> <font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D9" onmouseover="rs('pre_poly/D9')" onmouseout="rh()">PRE_POLY:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E7:33_3_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D10" onmouseover="rs('pre_poly/D10')" onmouseout="rh()">PRE_POLY:def 10</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_3_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:33_3_1_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</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="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:33_3_1_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font> <a href="pre_poly.html#R2" title="PRE_POLY:pred.2">&lt;='</a> <font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</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"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:33_3"/>
<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="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c4">c</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>  <a href="pre_poly.html#K17" title="PRE_POLY:func.17">BagOrder</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D14" onmouseover="rs('pre_poly/D14')" onmouseout="rh()">PRE_POLY:def 14</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:33"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bagorder.html#NK4" title="BAGORDER:NK.4">LexOrder</a> <font color="Maroon" title="c1">n</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b3">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">b</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b3">c</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>  <a href="bagorder.html#NK4" title="BAGORDER:NK.4">LexOrder</a> <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"> verum</span><br/>


</div>
