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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">EqR1</font> <a href="eqrel_1.html#K4" title="EQREL_1:func.4">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">EqR1</font> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <font color="Olive" title="b2">EqR2</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">EqR1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">EqR1</font>, <font color="Maroon" title="c3">EqR2</font> be   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K4" title="EQREL_1:func.4">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <font color="Maroon" title="c3">EqR2</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">EqR1</font></span><br/>





<span class="kw">thus </span><a NAME="E1:27"/>
<font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K4" title="EQREL_1:func.4">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <font color="Maroon" title="c3">EqR2</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c2">EqR1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">EqR1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K4" title="EQREL_1:func.4">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <font color="Maroon" title="c3">EqR2</font></span>)</span></span><br/>

<a NAME="E2:27"/>
( <font color="Maroon" title="c2">EqR1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K3" title="EQREL_1:func.3">\/</a> <font color="Maroon" title="c3">EqR2</font> &amp; <font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K3" title="EQREL_1:func.3">\/</a> <font color="Maroon" title="c3">EqR2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <font color="Maroon" title="c3">EqR2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" target="_self" title="EQREL_1:def.3">Def3</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<a NAME="E3:27"/><span class="kw">then </span>
<font color="Maroon" title="c2">EqR1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <font color="Maroon" title="c3">EqR2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:27"/>
<font color="Maroon" title="c2">EqR1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K4" title="EQREL_1:func.4">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EqR1</font> <a href="eqrel_1.html#K5" title="EQREL_1:func.5">"\/"</a> <font color="Maroon" title="c3">EqR2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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