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<b>let </b><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b2">SH</font>, <font color="Olive" title="b3">SF</font>, <font color="Olive" title="b4">SG</font> being  <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Olive" title="b1">M</font>  st <font color="Olive" title="b2">SH</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b3">SF</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Olive" title="b4">SG</font> holds <br/> <a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Olive" title="b2">SH</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Olive" title="b3">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Olive" title="b4">SG</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">M</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">SH</font>, <font color="Olive" title="b2">SF</font>, <font color="Olive" title="b3">SG</font> being  <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Maroon" title="c2">M</font>  st <font color="Olive" title="b1">SH</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b2">SF</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Olive" title="b3">SG</font> holds <br/> <a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Olive" title="b1">SH</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Olive" title="b2">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Olive" title="b3">SG</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">SH</font>, <font color="Maroon" title="c4">SF</font>, <font color="Maroon" title="c5">SG</font> be   <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Maroon" title="c2">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">SH</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">SF</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">SG</font> implies  <a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span> )</span><br/>









<b>assume </b><a NAME="E1:72"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c3">SH</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">SF</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">SG</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> implies <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> )</span><br/><b>assume </b><a NAME="E1:72_1"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span><br/><b>then consider </b><font color="Maroon" title="c7">Qf</font> being   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span><b> such that </b><br/><a NAME="E3:72_1"/><i><font color="Green" title="E16">A3</font></i>: 
<font color="Maroon" title="c7">Qf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">SF</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
 <b>and </b><br/><a NAME="E4:72_1"/><i><font color="Green" title="E17">A4</font></i>: 
<span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c7">Qf</font>
 <b>by </b><i><a class="ref" href="mssubfam.html#D2" target="_self" title="MSSUBFAM:def.2">Def2</a></i>;<br/><b>consider </b><font color="Maroon" title="c8">Qg</font> being   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span><b> such that </b><br/><a NAME="E6:72_1"/><i><font color="Green" title="E18">A5</font></i>: 
<font color="Maroon" title="c8">Qg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">SG</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
 <b>and </b><br/><a NAME="E7:72_1"/><i><font color="Green" title="E19">A6</font></i>: 
<span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c8">Qg</font>
 <b>by </b><i><a class="txt" href="mssubfam.html#E1:72_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="mssubfam.html#D2" target="_self" title="MSSUBFAM:def.2">Def2</a></i>;<br/><b>consider </b><font color="Maroon" title="c9">Qh</font> being   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span><b> such that </b><br/><a NAME="E9:72_1"/><i><font color="Green" title="E20">A7</font></i>: 
<font color="Maroon" title="c9">Qh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">SH</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
 <b>and </b><br/><a NAME="E10:72_1"/><i><font color="Green" title="E21">A8</font></i>: 
<span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c9">Qh</font>
 <b>by </b><i><a class="txt" href="mssubfam.html#E1:72_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="mssubfam.html#D2" target="_self" title="MSSUBFAM:def.2">Def2</a></i>;<br/><a NAME="E11:72_1"/><i><font color="Green" title="E22">A9</font></i>: 
<font color="Maroon" title="c9">Qh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">Qf</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Qg</font>
 <b>by </b><i><a class="txt" href="mssubfam.html#E1:72"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="mssubfam.html#E1:72_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="mssubfam.html#E3:72_1"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="mssubfam.html#E6:72_1"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="mssubfam.html#E9:72_1"><i><font color="Green" title="E20">A7</font></i></a>, <a class="ref" href="pboole.html#D7" title="PBOOLE:def.7">PBOOLE:def 7</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="72_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:72_1_1_1"/>
( ( <font color="Maroon" title="c7">Qf</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">Qg</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) or ( <font color="Maroon" title="c7">Qf</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">Qg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) or ( <font color="Maroon" title="c7">Qf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">Qg</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) or ( <font color="Maroon" title="c7">Qf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">Qg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="72_1_1_1_1"><b>case </b></a><a NAME="E1:72_1_1_1_1"/><i><font color="Green" title="E23">A10</font></i>: 
( <font color="Maroon" title="c7">Qf</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">Qg</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span><br/><div class="add"><a NAME="E2:72_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c9">Qh</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="mssubfam.html#E11:72_1"><i><font color="Green" title="E22">A9</font></i></a>, <a class="ref" href="xboole_1.html#T15" title="XBOOLE_1:th.15">XBOOLE_1:15</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> = 
 <a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <font color="Maroon" title="c9">Qh</font>
<b>by </b><i><a class="txt" href="mssubfam.html#E10:72_1"><i><font color="Green" title="E21">A8</font></i></a>, <a class="ref" href="setfam_1.html#D10" title="SETFAM_1:def.10">SETFAM_1:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <font color="Maroon" title="c7">Qf</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <font color="Maroon" title="c8">Qg</font></span>)</span>
<b>by </b><i><a class="txt" href="mssubfam.html#E11:72_1"><i><font color="Green" title="E22">A9</font></i></a>, <a class="txt" href="mssubfam.html#E1:72_1_1_1_1"><i><font color="Green" title="E23">A10</font></i></a>, <a class="ref" href="setfam_1.html#T10" title="SETFAM_1:th.10">SETFAM_1:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <font color="Maroon" title="c8">Qg</font></span>)</span>
<b>by </b><i><a class="txt" href="mssubfam.html#E4:72_1"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="mssubfam.html#E1:72_1_1_1_1"><i><font color="Green" title="E23">A10</font></i></a>, <a class="ref" href="setfam_1.html#D10" title="SETFAM_1:def.10">SETFAM_1:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>
<b>by </b><i><a class="txt" href="mssubfam.html#E7:72_1"><i><font color="Green" title="E19">A6</font></i></a>, <a class="txt" href="mssubfam.html#E1:72_1_1_1_1"><i><font color="Green" title="E23">A10</font></i></a>, <a class="ref" href="setfam_1.html#D10" title="SETFAM_1:def.10">SETFAM_1:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
<b>by </b><i><a class="txt" href="mssubfam.html#E1:72_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="pboole.html#D8" title="PBOOLE:def.8">PBOOLE:def 8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="72_1_1_1_2"><b>case </b></a><a NAME="E1:72_1_1_1_2"/><i><font color="Green" title="E23">A11</font></i>: 
( <font color="Maroon" title="c7">Qf</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">Qg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>
<b>by </b><i><a class="txt" href="mssubfam.html#E4:72_1"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="mssubfam.html#E10:72_1"><i><font color="Green" title="E21">A8</font></i></a>, <a class="txt" href="mssubfam.html#E11:72_1"><i><font color="Green" title="E22">A9</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>
<b>by </b><i><a class="txt" href="mssubfam.html#E7:72_1"><i><font color="Green" title="E19">A6</font></i></a>, <a class="txt" href="mssubfam.html#E1:72_1_1_1_2"><i><font color="Green" title="E23">A11</font></i></a>, <a class="ref" href="setfam_1.html#D10" title="SETFAM_1:def.10">SETFAM_1:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
<b>by </b><i><a class="txt" href="mssubfam.html#E1:72_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="pboole.html#D8" title="PBOOLE:def.8">PBOOLE:def 8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="72_1_1_1_3"><b>case </b></a><a NAME="E1:72_1_1_1_3"/><i><font color="Green" title="E23">A12</font></i>: 
( <font color="Maroon" title="c7">Qf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">Qg</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>
<b>by </b><i><a class="txt" href="mssubfam.html#E7:72_1"><i><font color="Green" title="E19">A6</font></i></a>, <a class="txt" href="mssubfam.html#E10:72_1"><i><font color="Green" title="E21">A8</font></i></a>, <a class="txt" href="mssubfam.html#E11:72_1"><i><font color="Green" title="E22">A9</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>
<b>by </b><i><a class="txt" href="mssubfam.html#E4:72_1"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="mssubfam.html#E1:72_1_1_1_3"><i><font color="Green" title="E23">A12</font></i></a>, <a class="ref" href="setfam_1.html#D10" title="SETFAM_1:def.10">SETFAM_1:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
<b>by </b><i><a class="txt" href="mssubfam.html#E1:72_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="pboole.html#D8" title="PBOOLE:def.8">PBOOLE:def 8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="72_1_1_1_4"><b>case </b></a><a NAME="E1:72_1_1_1_4"/>
( <font color="Maroon" title="c7">Qf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">Qg</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> = 
<span class="p1">(<span class="default"><a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c7">Qf</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c8">Qg</font></span>)</span>
<b>by </b><i><a class="txt" href="mssubfam.html#E10:72_1"><i><font color="Green" title="E21">A8</font></i></a>, <a class="txt" href="mssubfam.html#E11:72_1"><i><font color="Green" title="E22">A9</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
<b>by </b><i><a class="txt" href="mssubfam.html#E1:72_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="mssubfam.html#E4:72_1"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="mssubfam.html#E7:72_1"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="pboole.html#D8" title="PBOOLE:def.8">PBOOLE:def 8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E13:72_1"/>
<span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p2">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:72"/>
 <a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c3">SH</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c4">SF</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K6" title="MSSUBFAM:func.6">meet</a> <font color="Maroon" title="c5">SG</font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
