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<a NAME="E1:33_1_1"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="waybel_3.html#K3" title="WAYBEL_3:func.3">.</a> <font color="Olive" title="b1">i</font> is  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_1.html#V9" title="WAYBEL_1:attr.9">Heyting</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E2:33_1_1"/><b>then </b>
(  <a href="yellow_1.html#K5" title="YELLOW_1:func.5">product</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <font color="Maroon" title="c2">R</font></span>)</span> is <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> &amp;  <a href="yellow_1.html#K5" title="YELLOW_1:func.5">product</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <font color="Maroon" title="c2">R</font></span>)</span> is <a href="waybel_1.html#V9" title="WAYBEL_1:attr.9">Heyting</a> )
 
<b>by </b><i><a class="ref" href="lfuzzy_0.html#T13" target="_self" title="LFUZZY_0:th.13">Th13</a></i>;<br/>
<b>hence </b><a NAME="E3:33_1_1"/>
<font color="Maroon" title="c2">R</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> <font color="Maroon" title="c1">A</font> is <a href="waybel_1.html#V9" title="WAYBEL_1:attr.9">Heyting</a>
 <b>by </b><i><a class="ref" href="yellow_1.html#D5" title="YELLOW_1:def.5">YELLOW_1:def 5</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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