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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:23"/>
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) &amp; <font color="Maroon">c<sub>1</sub></font> <a href="lattice3.html#K7" target="_self">~</a>  <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relset_1.html#K6">~</a> </span>)</span> #) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> implies <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> ) &amp; ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> ) &amp; ( <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K8" target="_self">~</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8" target="_self">~</a>  implies <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K8" target="_self">~</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8" target="_self">~</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice3.html#K7" target="_self">~</a> </span>)</span> ) &amp; ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K8" target="_self">~</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8" target="_self">~</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice3.html#K7" target="_self">~</a> </span>)</span> implies <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K8" target="_self">~</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8" target="_self">~</a>  ) &amp; ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> implies <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relset_1.html#K6">~</a>  ) &amp; ( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relset_1.html#K6">~</a>  implies <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> ) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8" target="_self">~</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K8" target="_self">~</a>  )
 
<b>by </b><i><a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a>, <a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/>
<b>hence </b><a NAME="E2:23"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> iff <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K8" target="_self">~</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8" target="_self">~</a>  )
 ;<br/>


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