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<b>consider </b><font color="Maroon" title="c5">L</font> being  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="c2">A</font><b> such that </b><br/><a NAME="E2:32_1_1"/><i><font color="Green" title="E31">A2</font></i>: 
(  <a href="pencil_1.html#K3" title="PENCIL_1:func.3">indx</a> <font color="Maroon" title="c5">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font> &amp;  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c5">L</font> is    <a href="pencil_2.html#M1" title="PENCIL_2:mode.1">Segre-Coset</a> of <font color="Maroon" title="c2">A</font> )
 <b>by </b><i><a class="ref" href="pencil_3.html#T8" target="_self" title="PENCIL_3:th.8">Th8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">n</font> =  <a href="pencil_3.html#K3" title="PENCIL_3:func.3">canonical_embedding</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c5">L</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K2" title="PENCIL_1:func.2">.</a> <font color="Maroon" title="c4">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="pencil_1.html#K2" title="PENCIL_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pencil_3.html#K2" title="PENCIL_3:func.2">permutation_of_indices</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">i</font></span>)</span></span>)</span> <b>by </b><i><a class="txt" href="pencil_3.html#E2:32_1_1"><i><font color="Green" title="E31">A2</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">n</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b</font> being 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="c2">A</font>  st  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Olive" title="b1">b</font> is    <a href="pencil_2.html#M1" title="PENCIL_2:mode.1">Segre-Coset</a> of <font color="Maroon" title="c2">A</font> &amp;  <a href="pencil_1.html#K3" title="PENCIL_1:func.3">indx</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font> holds <br/><font color="Maroon" title="c6">n</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="pencil_3.html#K3" title="PENCIL_3:func.3">canonical_embedding</a> <font color="Maroon" title="c3">f</font>,<font color="Olive" title="b1">b</font></span><br/>

<b>let </b><font color="Maroon" title="c7">b</font> be  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="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c7">b</font> is    <a href="pencil_2.html#M1" title="PENCIL_2:mode.1">Segre-Coset</a> of <font color="Maroon" title="c2">A</font> &amp;  <a href="pencil_1.html#K3" title="PENCIL_1:func.3">indx</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font> implies <font color="Maroon" title="c6">n</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="pencil_3.html#K3" title="PENCIL_3:func.3">canonical_embedding</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c7">b</font> )</span><br/>

<b>assume </b><a NAME="E4:32_1_1"/><i><font color="Green" title="E32">A3</font></i>: 
(  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c7">b</font> is    <a href="pencil_2.html#M1" title="PENCIL_2:mode.1">Segre-Coset</a> of <font color="Maroon" title="c2">A</font> &amp;  <a href="pencil_1.html#K3" title="PENCIL_1:func.3">indx</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">n</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="pencil_3.html#K3" title="PENCIL_3:func.3">canonical_embedding</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c7">b</font></span><br/>

<b>thus </b><a NAME="E5:32_1_1"/>
<font color="Maroon" title="c6">n</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="pencil_3.html#K3" title="PENCIL_3:func.3">canonical_embedding</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="pencil_3.html#E1:32"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="pencil_3.html#E2:32_1_1"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="pencil_3.html#E4:32_1_1"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="pencil_3.html#T27" target="_self" title="PENCIL_3:th.27">Th27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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