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<b>let </b><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L2</font> #) implies for <font color="Olive" title="b1">X1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L1</font><br/> for <font color="Olive" title="b2">X2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Olive" title="b1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">X2</font> holds <br/>( ( <font color="Olive" title="b1">X1</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> implies <font color="Olive" title="b2">X2</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> ) &amp; ( <font color="Olive" title="b1">X1</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> implies <font color="Olive" title="b2">X2</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> ) ) )</span><br/>

<b>assume </b><a NAME="E1:56"/><i><font color="Green" title="E29">A1</font></i>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L2</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">X1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L1</font><br/> for <font color="Olive" title="b2">X2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Olive" title="b1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">X2</font> holds <br/>( ( <font color="Olive" title="b1">X1</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> implies <font color="Olive" title="b2">X2</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> ) &amp; ( <font color="Olive" title="b1">X1</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> implies <font color="Olive" title="b2">X2</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> ) )</span><br/>

<b>let </b><font color="Maroon" title="c3">X1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L1</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">X2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Maroon" title="c3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X2</font> holds <br/>( ( <font color="Maroon" title="c3">X1</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> implies <font color="Olive" title="b1">X2</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> ) &amp; ( <font color="Maroon" title="c3">X1</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> implies <font color="Olive" title="b1">X2</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> ) )</span><br/><b>let </b><font color="Maroon" title="c4">X2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">L2</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">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</font> implies ( ( <font color="Maroon" title="c3">X1</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> implies <font color="Maroon" title="c4">X2</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> ) &amp; ( <font color="Maroon" title="c3">X1</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> implies <font color="Maroon" title="c4">X2</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> ) ) )</span><br/>



<b>assume </b><a NAME="E2:56"/><i><font color="Green" title="E30">A2</font></i>: 
<font color="Maroon" title="c3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</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">X1</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> implies <font color="Maroon" title="c4">X2</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> ) &amp; ( <font color="Maroon" title="c3">X1</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> implies <font color="Maroon" title="c4">X2</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> ) )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">X1</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> implies <font color="Maroon" title="c4">X2</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> )</span>
<div class="add"><b>assume </b><a NAME="E1:56_1"/>
<font color="Maroon" title="c3">X1</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">X2</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a></span><br/><a NAME="E2:56_1"/><b>then </b>
(  <a href="waybel_0.html#K3" title="WAYBEL_0:func.3">downarrow</a> <font color="Maroon" title="c3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel_0.html#K3" title="WAYBEL_0:func.3">downarrow</a> <font color="Maroon" title="c4">X2</font> &amp;  <a href="waybel_0.html#K3" title="WAYBEL_0:func.3">downarrow</a> <font color="Maroon" title="c3">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X1</font> )
 <b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="#E2:56"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="waybel_0.html#T13" target="_self" title="WAYBEL_0:th.13">Th13</a>, <a class="ref" href="waybel_0.html#T23" target="_self" title="WAYBEL_0:th.23">Th23</a></i>;<br/><b>hence </b><a NAME="E3:56_1"/>
<font color="Maroon" title="c4">X2</font> is <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a>
 <b>by </b><i><a class="txt" href="#E2:56"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="waybel_0.html#T23" target="_self" title="WAYBEL_0:th.23">Th23</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>
<b>end;</b></div>

<b>assume </b><a NAME="E4:56"/>
<font color="Maroon" title="c3">X1</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">X2</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a></span><br/>

<a NAME="E5:56"/><b>then </b>
(  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Maroon" title="c3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Maroon" title="c4">X2</font> &amp;  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Maroon" title="c3">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X1</font> )
 
<b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="#E2:56"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="waybel_0.html#T13" target="_self" title="WAYBEL_0:th.13">Th13</a>, <a class="ref" href="waybel_0.html#T24" target="_self" title="WAYBEL_0:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E6:56"/>
<font color="Maroon" title="c4">X2</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>
 <b>by </b><i><a class="txt" href="#E2:56"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="waybel_0.html#T24" target="_self" title="WAYBEL_0:th.24">Th24</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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