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<b>let </b><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> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font>;<br/><b>let </b><font color="Maroon" title="c3">A</font> be  <a href="pencil_1.html#V11" title="PENCIL_1:attr.11">TopStruct-yielding</a> <a href="pencil_1.html#V14" title="PENCIL_1:attr.14">non-Trivial-yielding</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>;<br/>





<a NAME="E1:8"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E2:8"/><b>then </b>
<font color="Maroon" title="c3">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></i>;<br/>
<a NAME="E3:8"/><b>then </b>
not <font color="Maroon" title="c3">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c2">x</font> is <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a>
 
<b>by </b><i><a class="ref" href="pencil_1.html#D18" title="PENCIL_1:def.18">PENCIL_1:def 18</a></i>;<br/>
<a NAME="E4:8"/><b>then </b>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 
<b>by </b><i><a class="ref" href="realset2.html#D5" title="REALSET2:def.5">REALSET2:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">C</font> =  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span> as  non <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>consider </b><font color="Maroon" title="c5">p0</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K5" title="PENCIL_1:func.5">Segre_Product</a> <font color="Maroon" title="c3">A</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">p0</font> = <font color="Maroon" title="c5">p0</font> as    <a href="pboole.html#M2" title="PBOOLE:mode.2">Element</a> of  <a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font> <b>by </b><i><a class="ref" href="pencil_3.html#T6" target="_self" title="PENCIL_3:th.6">Th6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">p</font> = <span class="p1"><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">{</a><span class="default"><font color="Maroon" title="c6">p0</font></span><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">}</a></span> as    <a href="pboole.html#M4" title="PBOOLE:mode.4">ManySortedSubset</a> of  <a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font> <b>by </b><i><a class="ref" href="pencil_1.html#T11" title="PENCIL_1:th.11">PENCIL_1:11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">b</font> = <font color="Maroon" title="c7">p</font> <a href="polynom1.html#K2" title="POLYNOM1:func.2">+*</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">C</font> as  non <a href="pencil_1.html#V13" title="PENCIL_1:attr.13">trivial-yielding</a> <a href="pencil_1.html#V16" title="PENCIL_1:attr.16">Segre-like</a>  <a href="pboole.html#M4" title="PBOOLE:mode.4">ManySortedSubset</a> of  <a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font> <b>by </b><i><a class="ref" href="pencil_1.html#T9" title="PENCIL_1:th.9">PENCIL_1:9</a>, <a class="ref" href="pencil_1.html#T10" title="PENCIL_1:th.10">PENCIL_1:10</a>, <a class="ref" href="pencil_2.html#T7" title="PENCIL_2:th.7">PENCIL_2:7</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c8">b</font>
;<br/>

<a NAME="E10:8"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E11:8"/><b>then </b><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c8">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C</font>
 
<b>by </b><i><a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>;<br/>
<b>hence </b><a NAME="E12:8"/>
 <a href="pencil_1.html#K3" title="PENCIL_1:func.3">indx</a> <font color="Maroon" title="c8">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="ref" href="pencil_1.html#D21" title="PENCIL_1:def.21">PENCIL_1:def 21</a></i>;<br/>

<a NAME="E13:8"/><b>then </b><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c8">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="pencil_1.html#K3" title="PENCIL_1:func.3">indx</a> <font color="Maroon" title="c8">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <span class="p2">(<span class="default"><a href="pencil_1.html#K3" title="PENCIL_1:func.3">indx</a> <font color="Maroon" title="c8">b</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="pencil_3.html#E11:8"><i><font color="Green" title="E8">A1</font></i></a></i>;<br/>
<a NAME="E14:8"/>
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c8">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K5" title="PENCIL_1:func.5">Segre_Product</a> <font color="Maroon" title="c3">A</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:8_1"/>
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c8">b</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c10">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E3:8_1"/><i><font color="Green" title="E10">A3</font></i>: 
( <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c8">b</font> &amp; ( for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c8">b</font> holds <br/><font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> ) )
 <b>by </b><i><a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/>
<a NAME="E4:8_1"/><i><font color="Green" title="E11">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E5:8_1"/><b>then </b><i><font color="Green" title="E12">A5</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pencil_3.html#E3:8_1"><i><font color="Green" title="E10">A3</font></i></a>, <a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:8_1_1"/><i><font color="Green" title="E13">A6</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font></span>)</span>
 ;<br/><a NAME="E2:8_1_1"/><b>then </b><i><font color="Green" title="E14">A7</font></i>: 
<font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font>
 <b>by </b><i><a class="txt" href="pencil_3.html#E3:8_1"><i><font color="Green" title="E10">A3</font></i></a>, <a class="txt" href="pencil_3.html#E5:8_1"><i><font color="Green" title="E12">A5</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c12">i1</font> = <font color="Maroon" title="c11">i</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font> <b>by </b><i><a class="txt" href="pencil_3.html#E4:8_1"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="pencil_3.html#E1:8_1_1"><i><font color="Green" title="E13">A6</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:8_1_1_1"/>
( <font color="Maroon" title="c12">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> or <font color="Maroon" title="c12">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_1_1_1"><b>suppose </b></a><a NAME="E1:8_1_1_1_1"/>
<font color="Maroon" title="c12">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:8_1_1_1_1"/>
<font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font>
 <b>by </b><i><a class="txt" href="pencil_3.html#E11:8"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="pencil_3.html#E2:8_1_1"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="pencil_3.html#T7" target="_self" title="PENCIL_3:th.7">Th7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_1_1_2"><b>suppose </b></a><a NAME="E1:8_1_1_1_2"/>
<font color="Maroon" title="c12">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x</font>
 ;<br/><div class="add"><a NAME="E2:8_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i1</font>
 <b>by </b><i><a class="txt" href="pencil_3.html#E2:8_1_1"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>;<br/><a NAME="E3:8_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">p0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="pzfmisc1.html#D1" title="PZFMISC1:def.1">PZFMISC1:def 1</a></i>;<br/><a NAME="E4:8_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">p0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i1</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E5:8_1_1_1_2"/><b>then </b><i><font color="Green" title="E15">A8</font></i>: 
<font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i1</font>
 <b>by </b><i><a class="ref" href="pboole.html#D17" title="PBOOLE:def.17">PBOOLE:def 17</a></i>;<br/><a NAME="E6:8_1_1_1_2"/>
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/><a NAME="E7:8_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c12">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></i>;<br/><a NAME="E8:8_1_1_1_2"/><b>then </b>
not <font color="Maroon" title="c3">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c12">i1</font> is <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a>
 <b>by </b><i><a class="ref" href="pencil_1.html#D18" title="PENCIL_1:def.18">PENCIL_1:def 18</a></i>;<br/><a NAME="E9:8_1_1_1_2"/><b>then </b>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c12">i1</font></span>)</span> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 <b>by </b><i><a class="ref" href="realset2.html#D5" title="REALSET2:def.5">REALSET2:def 5</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c13">AA</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c12">i1</font></span>)</span> as  non <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/><a NAME="E11:8_1_1_1_2"/>
not <font color="Maroon" title="c13">AA</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><a NAME="E12:8_1_1_1_2"/><b>then </b>
not  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="pencil_1.html#K1" title="PENCIL_1:func.1">.</a> <font color="Maroon" title="c12">i1</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><a NAME="E13:8_1_1_1_2"/><b>then </b>
not <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="pencil_3.html#T7" target="_self" title="PENCIL_3:th.7">Th7</a></i>;<br/><b>hence </b><a NAME="E14:8_1_1_1_2"/>
<font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font>
 <b>by </b><i><a class="txt" href="pencil_3.html#E5:8_1_1_1_2"><i><font color="Green" title="E15">A8</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E7:8_1"/><b>then </b><i><font color="Green" title="E13">A9</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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="c3">A</font></span>)</span>
 
<b>by </b><i><a class="txt" href="pencil_3.html#E3:8_1"><i><font color="Green" title="E10">A3</font></i></a>, <a class="txt" href="pencil_3.html#E5:8_1"><i><font color="Green" title="E12">A5</font></i></a>, <a class="ref" href="card_3.html#D5" title="CARD_3:def.5">CARD_3:def 5</a></i>;<br/>
<a NAME="E8:8_1"/>
 <a href="pencil_1.html#K5" title="PENCIL_1:func.5">Segre_Product</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p2">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pencil_1.html#K4" title="PENCIL_1:func.4">Segre_Blocks</a> <font color="Maroon" title="c3">A</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="pencil_1.html#D23" title="PENCIL_1:def.23">PENCIL_1:def 23</a></i>;<br/>
<b>hence </b><a NAME="E9:8_1"/>
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pencil_1.html#K5" title="PENCIL_1:func.5">Segre_Product</a> <font color="Maroon" title="c3">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="pencil_3.html#E7:8_1"><i><font color="Green" title="E13">A9</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E15:8"/>
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c8">b</font> is    <a href="pencil_2.html#M1" title="PENCIL_2:mode.1">Segre-Coset</a> of <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="pencil_3.html#E13:8"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="pencil_2.html#D2" title="PENCIL_2:def.2">PENCIL_2:def 2</a></i>;<br/>


</div>
