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

<span class="kw">let </span><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" 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">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S1</font><br/>  for <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S2</font> holds <br/> ( ( <font color="Olive" title="b1">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b2">c</font> &amp; <font color="Olive" title="b3">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b4">d</font> ) iff <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S2</font> holds <br/> ( ( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Olive" title="b1">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b2">d</font> ) iff <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Olive" title="b2">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">d</font> ) iff <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c7">I1</font> =  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">I2</font> =  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">S2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">x</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<a NAME="E1:25"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
( <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p3"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p3"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="yellow_3.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/>
<a NAME="E2:25"/><span class="lab"><font color="Green" title="E8">A2</font></span>: 
( <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p3"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p3"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="yellow_3.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/>
<a NAME="E3:25"/><span class="lab"><font color="Green" title="E9">A3</font></span>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<span class="kw">thus </span><a NAME="E4:25"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">d</font> implies <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> implies ( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">d</font> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:25_1"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">d</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><br/>

<a NAME="E2:25_1"/><span class="kw">then </span>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p5"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p5"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a></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>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S1</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p5"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p5"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p5"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></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>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">S2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="txt" href="#E2:25"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<a NAME="E3:25_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow_3.html#K2" title="YELLOW_3:func.2">["</a><span class="default"> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S1</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">S2</font></span><a href="yellow_3.html#K2" title="YELLOW_3:func.2">"]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="ref" href="yellow_3.html#T10" target="_self" title="YELLOW_3:th.10">Th10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:25_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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 <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_3.html#D2" target="_self" title="YELLOW_3:def.2">Def2</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a> <a class="txt" 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="E5:25"/>
<span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">d</font> )</span><br/>

<a NAME="E6:25"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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 <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<a NAME="E7:25"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>,<span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow_3.html#K2" title="YELLOW_3:func.2">["</a><span class="default"> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S1</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">S2</font></span><a href="yellow_3.html#K2" title="YELLOW_3:func.2">"]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_3.html#D2" target="_self" title="YELLOW_3:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:25"/>
( <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">c</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</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">S1</font> &amp; <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">d</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</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="c2">S2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="txt" href="#E2:25"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="yellow_3.html#T10" target="_self" title="YELLOW_3:th.10">Th10</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
