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<span class="kw">let </span><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a>   st <font color="Olive" title="b1">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Olive" title="b2">t</font>, <a href="partit_2.html#K1" title="PARTIT_2:func.1">{}</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>) holds <br/><font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font>, <font color="Maroon" title="c3">t</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c3">t</font>, <a href="partit_2.html#K1" title="PARTIT_2:func.1">{}</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>) implies <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:56"/>
<font color="Maroon" title="c2">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c3">t</font>, <a href="partit_2.html#K1" title="PARTIT_2:func.1">{}</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font></span><br/>

<a NAME="E2:56"/><span class="kw">then </span>
 <a href="rewrite2.html#K7" title="REWRITE2:func.7">==&gt;.-relation</a> <span class="p1">(<span class="default"><a href="partit_2.html#K1" title="PARTIT_2:func.1">{}</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>)</span>)</span> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>
 
;<br/>
<a NAME="E3:56"/><span class="kw">then </span>
 <a href="partit_2.html#K1" title="PARTIT_2:func.1">{}</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#T29" target="_self" onmouseover="rs('rewrite2/T29')" onmouseout="rh()">Th29</a></span>;<br/>
<a NAME="E4:56"/><span class="kw">then </span>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partit_2.html#D1" onmouseover="rs('partit_2/D1')" onmouseout="rh()">PARTIT_2:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:56"/>
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T13" onmouseover="rs('rewrite1/T13')" onmouseout="rh()">REWRITE1:13</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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