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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being   <a href="waybel_3.html#V4" title="WAYBEL_3:attr.4">non-Empty</a>   <a href="pencil_1.html#V11" title="PENCIL_1:attr.11">TopStruct-yielding</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  st (  for <font color="Olive" title="b2">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font> holds <br/> (  not <font color="Olive" title="b1">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Olive" title="b2">i</font> is  <a href="pencil_1.html#V4" title="PENCIL_1:attr.4">degenerated</a>  &amp;  not  for <font color="Olive" title="b3">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font> holds  <font color="Olive" title="b1">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Olive" title="b3">i</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  ) ) holds <br/> not  <a href="pencil_1.html#K5" title="PENCIL_1:func.5">Segre_Product</a> <font color="Olive" title="b1">A</font> is  <a href="pencil_1.html#V4" title="PENCIL_1:attr.4">degenerated</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="waybel_3.html#V4" title="WAYBEL_3:attr.4">non-Empty</a>   <a href="pencil_1.html#V11" title="PENCIL_1:attr.11">TopStruct-yielding</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font> holds <br/> (  not <font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Olive" title="b1">i</font> is  <a href="pencil_1.html#V4" title="PENCIL_1:attr.4">degenerated</a>  &amp;  not  for <font color="Olive" title="b2">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font> holds  <font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Olive" title="b2">i</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  ) ) implies  not  <a href="pencil_1.html#K5" title="PENCIL_1:func.5">Segre_Product</a> <font color="Maroon" title="c2">A</font> is  <a href="pencil_1.html#V4" title="PENCIL_1:attr.4">degenerated</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:50"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
 for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font> holds <br/> (  not <font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Olive" title="b1">i</font> is  <a href="pencil_1.html#V4" title="PENCIL_1:attr.4">degenerated</a>  &amp;  not  for <font color="Olive" title="b2">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font> holds  <font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Olive" title="b2">i</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="pencil_1.html#K5" title="PENCIL_1:func.5">Segre_Product</a> <font color="Maroon" title="c2">A</font> is  <a href="pencil_1.html#V4" title="PENCIL_1:attr.4">degenerated</a> </span><br/>

<a NAME="E2:50"/><span class="kw">then </span>
 not  <a href="pencil_1.html#K5" title="PENCIL_1:func.5">Segre_Product</a> <font color="Maroon" title="c2">A</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pencil_1.html#T15" target="_self" title="PENCIL_1:th.15">Th15</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">SB</font> =  <a href="pencil_1.html#K4" title="PENCIL_1:func.4">Segre_Blocks</a> <font color="Maroon" title="c2">A</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:50_1"/>
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">SB</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">B</font> being   <a href="pencil_1.html#V16" title="PENCIL_1:attr.16">Segre-like</a>   <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedSubset</a> of  <a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">A</font><span class="kw"> such that </span><br/><a NAME="E3:50_1"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c4">B</font>
 <span class="kw">and </span><br/><a NAME="E4:50_1"/><span class="lab"><font color="Green" title="E35">A3</font></span>: 
 ex <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font> st <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> is   <a href="pencil_1.html#NM1" title="PENCIL_1:NM.1">Block</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pencil_1.html#D22" target="_self" title="PENCIL_1:def.22">Def22</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c5">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font><span class="kw"> such that </span><br/><a NAME="E6:50_1"/><span class="lab"><font color="Green" title="E36">A4</font></span>: 
<font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> is   <a href="pencil_1.html#NM1" title="PENCIL_1:NM.1">Block</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c5">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:50_1"><span class="lab"><font color="Green" title="E35">A3</font></span></a></span>;<br/><a NAME="E7:50_1"/>
<font color="Maroon" title="c4">B</font> is  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:50_1"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="pencil_1.html#T1" target="_self" title="PENCIL_1:th.1">Th1</a></span>;<br/><a NAME="E8:50_1"/><span class="kw">then </span>
(  ex <font color="Olive" title="b1">R</font> being    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a>  st <br/>( <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c5">i</font> &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> ) &amp; <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> is   <a href="pencil_1.html#NM1" title="PENCIL_1:NM.1">Block</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c5">i</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:50_1"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="txt" href="#E6:50_1"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="ref" href="pralg_1.html#D13" title="PRALG_1:def.13">PRALG_1:def 13</a>, <a class="ref" href="pua2mss1.html#T2" title="PUA2MSS1:th.2">PUA2MSS1:2</a></span>;<br/><a NAME="E9:50_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c5">i</font> is  <a href="pencil_1.html#V4" title="PENCIL_1:attr.4">degenerated</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pencil_1.html#D5" target="_self" title="PENCIL_1:def.5">Def5</a></span>;<br/><span class="kw">hence </span><a NAME="E10:50_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E33">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E5:50"/><span class="kw">then </span>
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">A</font></span>)</span> is  not    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">SB</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E6:50"/>
 not  <a href="pencil_1.html#K5" title="PENCIL_1:func.5">Segre_Product</a> <font color="Maroon" title="c2">A</font> is  <a href="pencil_1.html#V4" title="PENCIL_1:attr.4">degenerated</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pencil_1.html#D5" target="_self" title="PENCIL_1:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
