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<span class="kw">let </span><font color="Maroon" title="c3">CS1</font>, <font color="Maroon" title="c4">CS2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="dist_1.html#K6" title="DIST_1:func.6">distribution_family</a> <font color="Maroon" title="c1">S</font>; <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"> ( <span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">CS1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> &amp; <span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">CS2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> implies <font color="Maroon" title="c3">CS1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">CS2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:24_1_2"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">CS1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 ; <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"> (  not <span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">CS2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> or <font color="Maroon" title="c3">CS1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">CS2</font> )</span><br/>

<a NAME="E2:24_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A4</font></span>: 
<font color="Maroon" title="c3">CS1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D2" onmouseover="rs('funct_1/D2')" onmouseout="rh()">FUNCT_1:def 2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:24_1_2"/><span class="lab"><font color="Green" title="E13">A5</font></span>: 
<span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">CS2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 ; <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="c3">CS1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">CS2</font></span><br/>

<a NAME="E4:24_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">CS2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D2" onmouseover="rs('funct_1/D2')" onmouseout="rh()">FUNCT_1:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:24_1_2"/>
<font color="Maroon" title="c3">CS1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">CS2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_2"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="txt" href="#E3:24_1_2"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E2:24_1_2"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="ref" href="funct_1.html#D4" onmouseover="rs('funct_1/D4')" onmouseout="rh()">FUNCT_1:def 4</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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