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<span class="kw">let </span><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</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">p1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font><br/>  for <font color="Olive" title="b2">p2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Maroon" title="c1">L1</font> is   <a href="latstone.html#V1" title="LATSTONE:attr.1">pseudocomplemented</a>  <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="latstone.html#V1" title="LATSTONE:attr.1">pseudocomplemented</a>  <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> holds <br/><span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">p1</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">p2</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">p1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</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">  for <font color="Olive" title="b1">p2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Maroon" title="c1">L1</font> is   <a href="latstone.html#V1" title="LATSTONE:attr.1">pseudocomplemented</a>  <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="latstone.html#V1" title="LATSTONE:attr.1">pseudocomplemented</a>  <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> holds <br/><span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Olive" title="b1">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p1</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">p2</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">p2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</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="c1">L1</font> is   <a href="latstone.html#V1" title="LATSTONE:attr.1">pseudocomplemented</a>  <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="latstone.html#V1" title="LATSTONE:attr.1">pseudocomplemented</a>  <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> implies <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p1</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">p2</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:69"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
( <font color="Maroon" title="c1">L1</font> is   <a href="latstone.html#V1" title="LATSTONE:attr.1">pseudocomplemented</a>  <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="latstone.html#V1" title="LATSTONE:attr.1">pseudocomplemented</a>  <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</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"> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p1</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">p2</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span></span><br/>

<a NAME="E2:69"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<font color="Maroon" title="c3">p1</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c3">p1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="latstone.html#D3" target="_self" onmouseover="rs('latstone/D3')" onmouseout="rh()">def3</a>, <a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E29">A1</font></span></a></span>;<br/>
<a NAME="E3:69"/>
<font color="Maroon" title="c4">p2</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="latstone.html#D3" target="_self" onmouseover="rs('latstone/D3')" onmouseout="rh()">def3</a>, <a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E29">A1</font></span></a></span>;<br/>
<a NAME="E4:69"/><span class="kw">then </span>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p1</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">p2</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="latstone.html#T29" target="_self" onmouseover="rs('latstone/T29')" onmouseout="rh()">ProductPsCompl</a>, <a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E29">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:69"/>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p1</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">p2</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="latstone.html#D3" target="_self" onmouseover="rs('latstone/D3')" onmouseout="rh()">def3</a>, <a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E29">A1</font></span></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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