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<span class="kw">let </span><font color="Maroon" title="c1">I</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">M</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><br/>  for <font color="Olive" title="b2">EqR1</font>, <font color="Olive" title="b3">EqR2</font> being   <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Olive" title="b1">M</font> holds  <font color="Olive" title="b2">EqR1</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Olive" title="b3">EqR2</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b2">EqR1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">M</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</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">EqR1</font>, <font color="Olive" title="b2">EqR2</font> being   <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Maroon" title="c2">M</font> holds  <font color="Olive" title="b1">EqR1</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Olive" title="b2">EqR2</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b1">EqR1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">EqR1</font>, <font color="Maroon" title="c4">EqR2</font> be   <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Maroon" title="c2">M</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="c3">EqR1</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">EqR1</font></span><br/>







<span class="kw">thus </span><a NAME="E1:15"/>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="pboole.html#D10" title="PBOOLE:def.10">PBOOLE:def 10</a> <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="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span></span><br/>

<a NAME="E2:15"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">EqR2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T14" title="PBOOLE:th.14">PBOOLE:14</a></span>;<br/>
<a NAME="E3:15"/>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_5.html#T4" target="_self" title="MSUALG_5:th.4">Th6</a></span>;<br/>
<a NAME="E4:15"/><span class="kw">then </span>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="pboole.html#T13" title="PBOOLE:th.13">PBOOLE:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:15"/>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T17" title="PBOOLE:th.17">PBOOLE:17</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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