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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#K5" title="EQREL_1:func.5">"\/"</a> <font color="Olive" title="b2">EqR2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="msualg_5.html#K1" title="MSUALG_5:func.1">EqCl</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">EqR1</font> <a href="eqrel_1.html#K3" title="EQREL_1:func.3">\/</a> <font color="Olive" title="b2">EqR2</font></span>)</span></span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="msualg_5.html#K1" title="MSUALG_5:func.1">EqCl</a> <span class="p1">(<span class="default"><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></span>)</span></span><br/>





<a NAME="E1:2"/>
( <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> &amp; ( for <font color="Olive" title="b1">EqR3</font> being  <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c1">X</font>  st <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="Olive" title="b1">EqR3</font> holds <br/><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> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">EqR3</font> ) )
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E2:2"/>
<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> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="msualg_5.html#K1" title="MSUALG_5:func.1">EqCl</a> <span class="p1">(<span class="default"><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></span>)</span>
 <b>by </b><i><a class="ref" href="msualg_5.html#D1" target="_self" title="MSUALG_5:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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