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<span class="kw">let </span><font color="Maroon" title="c1">U2</font>, <font color="Maroon" title="c2">U1</font>, <font color="Maroon" title="c3">U3</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/>  for <font color="Olive" title="b2">U</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">U2</font><br/>  for <font color="Olive" title="b3">P</font> being   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c2">U1</font>,<font color="Olive" title="b2">U</font><br/>  for <font color="Olive" title="b4">Q</font> being   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c1">U2</font>,<font color="Maroon" title="c3">U3</font> holds  <font color="Olive" title="b1">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Olive" title="b4">Q</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Olive" title="b3">P</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Olive" title="b4">Q</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">U</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">U2</font><br/>  for <font color="Olive" title="b2">P</font> being   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c2">U1</font>,<font color="Olive" title="b1">U</font><br/>  for <font color="Olive" title="b3">Q</font> being   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c1">U2</font>,<font color="Maroon" title="c3">U3</font> holds  <font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Olive" title="b3">Q</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Olive" title="b2">P</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Olive" title="b3">Q</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">U</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">U2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c2">U1</font>,<font color="Maroon" title="c5">U</font><br/>  for <font color="Olive" title="b2">Q</font> being   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c1">U2</font>,<font color="Maroon" title="c3">U3</font> holds  <font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Olive" title="b2">Q</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Olive" title="b1">P</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Olive" title="b2">Q</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">P</font> be   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c2">U1</font>,<font color="Maroon" title="c5">U</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Q</font> being   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c1">U2</font>,<font color="Maroon" title="c3">U3</font> holds  <font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Olive" title="b1">Q</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c6">P</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Olive" title="b1">Q</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">Q</font> be   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c1">U2</font>,<font color="Maroon" title="c3">U3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c7">Q</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c6">P</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c7">Q</font></span>)</span></span><br/>













<span class="kw">set </span><font color="Maroon" title="c8">R</font> = <font color="Maroon" title="c6">P</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c7">Q</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">LH</font> = <font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c7">Q</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">Pn</font> = <font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c6">P</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">Qn</font> = <font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c7">Q</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">RH</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c6">P</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c7">Q</font></span>)</span>;<br/>
<a NAME="E1:83"/>
( <font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c7">Q</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c6">P</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c7">Q</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c6">P</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c7">Q</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c7">Q</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel3.html#E33"><span class="lab"><font color="Green" title="E25">Lm12</font></span></a>, <a class="txt" href="fomodel3.html#E34"><span class="lab"><font color="Green" title="E26">Lm18</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:83"/>
<font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P</font> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <font color="Maroon" title="c7">Q</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c6">P</font></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="fomodel3.html#K8" title="FOMODEL3:func.8">-placesOf</a> <font color="Maroon" title="c7">Q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>; <a class="txt" 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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