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<span class="kw">let </span><font color="Maroon" title="c3">IT1</font>, <font color="Maroon" title="c4">IT2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c3">IT1</font> <a href="waybel_4.html#R2" title="WAYBEL_4:pred.2">is_maximal_wrt</a> <font color="Maroon" title="c2">X</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c4">IT2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c4">IT2</font> <a href="waybel_4.html#R2" title="WAYBEL_4:pred.2">is_maximal_wrt</a> <font color="Maroon" title="c2">X</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font> implies <font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:57_2_2"/><span class="lab"><font color="Green" title="E35">A11</font></span>: 
<font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <span class="kw">and </span><br/><a NAME="E2:57_2_2"/><span class="lab"><font color="Green" title="E36">A12</font></span>: 
<font color="Maroon" title="c3">IT1</font> <a href="waybel_4.html#R2" title="WAYBEL_4:pred.2">is_maximal_wrt</a> <font color="Maroon" title="c2">X</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>
 <span class="kw">and </span><br/><a NAME="E3:57_2_2"/><span class="lab"><font color="Green" title="E37">A13</font></span>: 
<font color="Maroon" title="c4">IT2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <span class="kw">and </span><br/><a NAME="E4:57_2_2"/><span class="lab"><font color="Green" title="E38">A14</font></span>: 
<font color="Maroon" title="c4">IT2</font> <a href="waybel_4.html#R2" title="WAYBEL_4:pred.2">is_maximal_wrt</a> <font color="Maroon" title="c2">X</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT2</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">IR</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>;<br/>
<a NAME="E5:57_2_2"/><span class="lab"><font color="Green" title="E39">A15</font></span>: 
( <font color="Maroon" title="c3">IT1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">IT2</font> or <font color="Maroon" title="c4">IT2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">IT1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#D29" title="WAYBEL_0:def.29">WAYBEL_0:def 29</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:57_2_2_1"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">IT1</font>,<font color="Maroon" title="c4">IT2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font> or <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">IT2</font>,<font color="Maroon" title="c3">IT1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:57_2_2"><span class="lab"><font color="Green" title="E39">A15</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_2_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:57_2_2_1_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">IT1</font>,<font color="Maroon" title="c4">IT2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT2</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:57_2_2_1_1"/>
<font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57_2_2"><span class="lab"><font color="Green" title="E36">A12</font></span></a>, <a class="txt" href="#E3:57_2_2"><span class="lab"><font color="Green" title="E37">A13</font></span></a>, <a class="ref" href="waybel_4.html#D24" title="WAYBEL_4:def.24">WAYBEL_4:def 24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="57_2_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:57_2_2_1_2"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">IT2</font>,<font color="Maroon" title="c3">IT1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT2</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:57_2_2_1_2"/>
<font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57_2_2"><span class="lab"><font color="Green" title="E35">A11</font></span></a>, <a class="txt" href="#E4:57_2_2"><span class="lab"><font color="Green" title="E38">A14</font></span></a>, <a class="ref" href="waybel_4.html#D24" title="WAYBEL_4:def.24">WAYBEL_4:def 24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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