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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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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  for <font color="Olive" title="b1">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> holds  <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Olive" title="b1">b</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:115"/><span class="lab"><font color="Green" title="E61">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> holds  <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Olive" title="b1">b</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font></span><br/>

<a NAME="E2:115"/>
<span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="orders_2.html#T1" onmouseover="rs('orders_2/T1')" onmouseout="rh()">ORDERS_2:1</a></span>;<br/>
<a NAME="E3:115"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="waybel_1.html#T67" target="_self" onmouseover="rs('waybel_1/T67')" onmouseout="rh()">Th67</a></span>;<br/>
<a NAME="E4:115"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A2</font></span>: 
<span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="waybel_1.html#T4" target="_self" onmouseover="rs('waybel_1/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E5:115"/>
<span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="waybel_1.html#T72" target="_self" onmouseover="rs('waybel_1/T72')" onmouseout="rh()">Th72</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:115"/>
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="txt" href="#E4:115"><span class="lab"><font color="Green" title="E62">A2</font></span></a>, <a class="ref" href="orders_2.html#T2" onmouseover="rs('orders_2/T2')" onmouseout="rh()">ORDERS_2:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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