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<b>let </b><font color="Maroon">I</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be  <a href="waybel_3.html#V4">non-Empty</a> <a href="pencil_1.html#V11" target="_self">TopStruct-yielding</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>



<b>assume </b><a NAME="E1:52"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font> holds <br/> ( not <font color="Maroon">A</font> <a href="pencil_1.html#K1" target="_self">.</a> <font color="Olive">i</font> is <a href="pencil_1.html#V4" target="_self">degenerated</a> &amp; not for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font> holds  <font color="Maroon">A</font> <a href="pencil_1.html#K1" target="_self">.</a> <font color="Olive">i</font> is <a href="pencil_1.html#V3" target="_self">void</a> )
 ;<br/>

<a NAME="E2:52"/>
not  <a href="pencil_1.html#K5" target="_self">Segre_Product</a> <font color="Maroon">A</font> is <a href="pencil_1.html#V3" target="_self">void</a>
 
<b>by </b><i>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">SB</font> =  <a href="pencil_1.html#K4" target="_self">Segre_Blocks</a> <font color="Maroon">A</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:52_1"/>
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12">Carrier</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">SB</font>
 ;<br/><b>then consider </b><font color="Maroon">B</font> being  <a href="pencil_1.html#V16" target="_self">Segre-like</a>  <a href="pboole.html#M4">ManySortedSubset</a> of  <a href="pralg_1.html#K12">Carrier</a> <font color="Maroon">A</font><b> such that </b><br/><a NAME="E3:52_1"/><i><font color="Green">E35</font></i>: 
(  <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12">Carrier</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">B</font> &amp;  ex <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font> st <font color="Maroon">B</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> is   <a href="pencil_1.html#NM1">Block</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="pencil_1.html#K1" target="_self">.</a> <font color="Olive">i</font></span>)</span> )
 <b>by </b><i><a class="ref" href="pencil_1.html#T1" target="_self">Th1</a></i>;<br/><b>consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font><b> such that </b><br/><a NAME="E5:52_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">B</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is   <a href="pencil_1.html#NM1">Block</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="pencil_1.html#K1" target="_self">.</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">R</font> being    <a href="struct_0.html#L1">1-sorted</a> <b> such that </b><br/><a NAME="E7:52_1"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="pencil_1.html#K1" target="_self">.</a> <font color="Maroon">i</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12">Carrier</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="pralg_1.html#D13">PRALG_1:def 13</a></i>;<br/><a NAME="E8:52_1"/>
<font color="Maroon">B</font> is <a href="relat_1.html#V2">non-empty</a>
 <b>by </b><i>, </i>;<br/><a NAME="E9:52_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="pralg_1.html#K12">Carrier</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is   <a href="pencil_1.html#NM1">Block</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="pencil_1.html#K1" target="_self">.</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="pencil_1.html#E5:52_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="pua2mss1.html#T2">PUA2MSS1:2</a></i>;<br/><a NAME="E10:52_1"/><b>then </b>
<font color="Maroon">A</font> <a href="pencil_1.html#K1" target="_self">.</a> <font color="Maroon">i</font> is <a href="pencil_1.html#V4" target="_self">degenerated</a>
 <b>by </b><i><a class="txt" href="pencil_1.html#E7:52_1"><i><font color="Green">E38</font></i></a>, </i>;<br/><b>hence </b><a NAME="E11:52_1"/>
contradiction
 <b>by </b><i><a class="txt" href="pencil_1.html#E3:52_1"><i><font color="Green">E35</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:52"/><b>then </b>
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12">Carrier</a> <font color="Maroon">A</font></span>)</span> is  not    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">SB</font>
 
;<br/>
<b>hence </b><a NAME="E6:52"/>
not  <a href="pencil_1.html#K5" target="_self">Segre_Product</a> <font color="Maroon">A</font> is <a href="pencil_1.html#V4" target="_self">degenerated</a>
 <b>by </b><i/>;<br/>


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