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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> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:26"/><i><font color="Green" title="E15">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> #)
 <b>and </b><br/><a NAME="E2:26"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c1">L1</font> is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>;<br/><b>reconsider </b><font color="Maroon" title="c6">x'</font> = <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c7">y'</font> = <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c8">z'</font> = <font color="Maroon" title="c5">z</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font> <b>by </b><i><a class="txt" href="waybel_8.html#E1:26"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/><b>assume </b><a NAME="E2:26_1"/>
( <font color="Maroon" title="c3">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">y</font> &amp; <font color="Maroon" title="c4">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">z</font> )
 ;<br/><a NAME="E3:26_1"/><b>then </b>
( <font color="Maroon" title="c6">x'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">y'</font> &amp; <font color="Maroon" title="c7">y'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c8">z'</font> )
 <b>by </b><i><a class="txt" href="waybel_8.html#E1:26"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="yellow_0.html#T1" title="YELLOW_0:th.1">YELLOW_0:1</a></i>;<br/><a NAME="E4:26_1"/><b>then </b>
<font color="Maroon" title="c6">x'</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c8">z'</font>
 <b>by </b><i><a class="txt" href="waybel_8.html#E2:26"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="yellow_0.html#D2" title="YELLOW_0:def.2">YELLOW_0:def 2</a></i>;<br/><b>hence </b><a NAME="E5:26_1"/>
<font color="Maroon" title="c3">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">z</font>
 <b>by </b><i><a class="txt" href="waybel_8.html#E1:26"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="yellow_0.html#T1" title="YELLOW_0:th.1">YELLOW_0:1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:26"/>
<font color="Maroon" title="c2">L2</font> is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>
 <b>by </b><i><a class="ref" href="yellow_0.html#D2" title="YELLOW_0:def.2">YELLOW_0:def 2</a></i>;<br/>


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