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<span class="kw">let </span><font color="Maroon" title="c1">H</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"> ( <font color="Maroon" title="c1">H</font> is  <a href="waybel_1.html#V9" title="WAYBEL_1:attr.9">Heyting</a>  implies <font color="Maroon" title="c1">H</font> is  <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:110"/><span class="lab"><font color="Green" title="E70">A1</font></span>: 
<font color="Maroon" title="c1">H</font> is  <a href="waybel_1.html#V9" title="WAYBEL_1:attr.9">Heyting</a> 
 ; <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="c1">H</font> is  <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">a</font> =  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>;<br/>
<span class="kw">take </span>
 the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a>  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="yellow_0.html#D5" title="YELLOW_0:def.5">YELLOW_0:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">H</font> <a href="lattice3.html#R2" title="LATTICE3:pred.2">is_&lt;=_than</a>  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a>  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lattice3.html#D9" title="LATTICE3:def.9">LATTICE3:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">H</font> or <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a>  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a>  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:110"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">H</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">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a>  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a>  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font></span><br/>

<a NAME="E3:110"/>
 the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a>  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110"><span class="lab"><font color="Green" title="E70">A1</font></span></a>, <a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:110"/>
<font color="Maroon" title="c3">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a>  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a>  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110"><span class="lab"><font color="Green" title="E70">A1</font></span></a>, <a class="ref" href="waybel_1.html#T67" target="_self" title="WAYBEL_1:th.67">Th70</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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