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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</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="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c2">B</font> iff <font color="Maroon" title="c1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">B</font> )</span><br/>



<a NAME="E1:133"/><span class="lab"><font color="Green" title="E105">A1</font></span>: 
(  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a>  <a href="surrealn.html#K8" title="SURREALN:func.8">No_Ordinal_op</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c2">B</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a>  <a href="surrealn.html#K8" title="SURREALN:func.8">No_Ordinal_op</a> <font color="Maroon" title="c2">B</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealn.html#T73" target="_self" onmouseover="rs('surrealn/T73')" onmouseout="rh()">Th73</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:133"/>
(  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c2">B</font> implies <font color="Maroon" title="c1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">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="c1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">B</font> implies  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c2">B</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="133_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:133_1"/>
 <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c2">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="c1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">B</font></span><br/>

<a NAME="E2:133_1"/><span class="kw">then </span>
 <a href="surrealn.html#K8" title="SURREALN:func.8">No_Ordinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c2">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:133"><span class="lab"><font color="Green" title="E105">A1</font></span></a>, <a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</a></span>;<br/>
<a NAME="E3:133_1"/><span class="kw">then </span>
 <a href="surrealn.html#K8" title="SURREALN:func.8">No_Ordinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a>  <a href="surrealn.html#K8" title="SURREALN:func.8">No_Ordinal_op</a> <font color="Maroon" title="c2">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:133"><span class="lab"><font color="Green" title="E105">A1</font></span></a>, <a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:133_1"/>
<font color="Maroon" title="c1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="surrealn.html#T68" target="_self" onmouseover="rs('surrealn/T68')" onmouseout="rh()">Th68</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">assume </span><a NAME="E3:133"/>
<font color="Maroon" title="c1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">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">  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c2">B</font></span><br/>

<a NAME="E4:133"/><span class="kw">then </span>
 <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a>  <a href="surrealn.html#K8" title="SURREALN:func.8">No_Ordinal_op</a> <font color="Maroon" title="c2">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealn.html#T68" target="_self" onmouseover="rs('surrealn/T68')" onmouseout="rh()">Th68</a>, <a class="txt" href="#E1:133"><span class="lab"><font color="Green" title="E105">A1</font></span></a>, <a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:133"/>
 <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c2">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:133"><span class="lab"><font color="Green" title="E105">A1</font></span></a>, <a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</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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