<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</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">H1</font>, <font color="Olive" title="b2">H2</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b3">h1</font>, <font color="Olive" title="b4">h2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_4.html#K11" title="GROUP_4:func.11">lattice</a> <font color="Maroon" title="c1">G</font></span>)</span>  st <font color="Olive" title="b3">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> &amp; <font color="Olive" title="b4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H2</font> holds <br/><font color="Olive" title="b3">h1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b4">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Olive" title="b2">H2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">H1</font>, <font color="Maroon" title="c3">H2</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</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">h1</font>, <font color="Olive" title="b2">h2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_4.html#K11" title="GROUP_4:func.11">lattice</a> <font color="Maroon" title="c1">G</font></span>)</span>  st <font color="Olive" title="b1">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> &amp; <font color="Olive" title="b2">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H2</font> holds <br/><font color="Olive" title="b1">h1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">H2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">h1</font>, <font color="Maroon" title="c5">h2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_4.html#K11" title="GROUP_4:func.11">lattice</a> <font color="Maroon" title="c1">G</font></span>)</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"> ( <font color="Maroon" title="c4">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> &amp; <font color="Maroon" title="c5">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H2</font> implies <font color="Maroon" title="c4">h1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">H2</font> )</span><br/>





<a NAME="E1:22"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c4">h1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_4.html#K9" title="GROUP_4:func.9">SubJoin</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c4">h1</font>,<font color="Maroon" title="c5">h2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D1" onmouseover="rs('lattices/D1')" onmouseout="rh()">LATTICES:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:22"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
( <font color="Maroon" title="c4">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> &amp; <font color="Maroon" title="c5">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H2</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="c4">h1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">H2</font></span><br/>

<a NAME="E3:22"/><span class="kw">then </span>
( <font color="Maroon" title="c2">H1</font> is  <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  &amp; <font color="Maroon" title="c3">H2</font> is  <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#D1" onmouseover="rs('group_3/D1')" onmouseout="rh()">GROUP_3:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:22"/>
<font color="Maroon" title="c4">h1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="group_4.html#D10" onmouseover="rs('group_4/D10')" onmouseout="rh()">GROUP_4:def 10</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/>


</div>
