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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">O</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">G</font> being  <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font><br/> for <font color="Olive" title="b2">s1</font>, <font color="Olive" title="b3">s2</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Olive" title="b1">G</font>  ex <font color="Olive" title="b4">s19</font>, <font color="Olive" title="b5">s29</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Olive" title="b1">G</font> st <br/>( <font color="Olive" title="b4">s19</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Olive" title="b2">s1</font> &amp; <font color="Olive" title="b5">s29</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Olive" title="b3">s2</font> &amp; <font color="Olive" title="b4">s19</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Olive" title="b5">s29</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font>  ex <font color="Olive" title="b3">s19</font>, <font color="Olive" title="b4">s29</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font> st <br/>( <font color="Olive" title="b3">s19</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Olive" title="b1">s1</font> &amp; <font color="Olive" title="b4">s29</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Olive" title="b2">s2</font> &amp; <font color="Olive" title="b3">s19</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Olive" title="b4">s29</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">s1</font>, <font color="Maroon" title="c4">s2</font> be   <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">s19</font>, <font color="Olive" title="b2">s29</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font> st <br/>( <font color="Olive" title="b1">s19</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Olive" title="b2">s29</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Olive" title="b1">s19</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Olive" title="b2">s29</font> )</span><br/>







<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:200_1"/>
( (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">s2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 ) or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">s2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_1"><span class="kw">suppose </span></a><a NAME="E1:200_1_1"/><span class="lab"><font color="Green" title="E173">A1</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">s2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">s19</font>, <font color="Olive" title="b2">s29</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font> st <br/>( <font color="Olive" title="b1">s19</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Olive" title="b2">s29</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Olive" title="b1">s19</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Olive" title="b2">s29</font> )</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c5">s29</font> =  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c3">s1</font>;<br/><span class="kw">set </span><font color="Maroon" title="c6">s19</font> =  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font>;<br/><span class="kw">take </span>
 <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">s29</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font> st <br/>(  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Olive" title="b1">s29</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp;  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Olive" title="b1">s29</font> )</span><br/><span class="kw">take </span>
 <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c3">s1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp;  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c3">s1</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp;  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a>  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c3">s1</font> )</span><br/><span class="kw">thus </span><a NAME="E2:200_1_1"/>
(  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp;  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c3">s1</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:200_1_1"><span class="lab"><font color="Green" title="E173">A1</font></span></a>, <a class="ref" href="group_9.html#T116" target="_self" title="GROUP_9:th.116">Th116</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a>  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c3">s1</font></span><br/><span class="kw">thus </span><a NAME="E3:200_1_1"/>
 <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a>  <a href="group_9.html#K21" title="GROUP_9:func.21">the_schreier_series_of</a> <font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c3">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:200_1_1"><span class="lab"><font color="Green" title="E173">A1</font></span></a>, <a class="ref" href="group_9.html#T117" target="_self" title="GROUP_9:th.117">Th117</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_2"><span class="kw">suppose </span></a><a NAME="E1:200_1_2"/><span class="lab"><font color="Green" title="E173">A2</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">s2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">s19</font>, <font color="Olive" title="b2">s29</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font> st <br/>( <font color="Olive" title="b1">s19</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Olive" title="b2">s29</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Olive" title="b1">s19</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Olive" title="b2">s29</font> )</span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:200_1_2_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">s2</font> or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">s2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:200_1_2_1_1"/><span class="lab"><font color="Green" title="E174">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">s2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">s19</font>, <font color="Olive" title="b2">s29</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font> st <br/>( <font color="Olive" title="b1">s19</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Olive" title="b2">s29</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Olive" title="b1">s19</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Olive" title="b2">s29</font> )</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c5">s29</font> = <font color="Maroon" title="c4">s2</font>;<br/><span class="kw">set </span><font color="Maroon" title="c6">s19</font> = <font color="Maroon" title="c4">s2</font>;<br/><span class="kw">take </span>
<font color="Maroon" title="c4">s2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">s29</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font> st <br/>( <font color="Maroon" title="c4">s2</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Olive" title="b1">s29</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Maroon" title="c4">s2</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Olive" title="b1">s29</font> )</span><br/><span class="kw">take </span>
<font color="Maroon" title="c4">s2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">s2</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Maroon" title="c4">s2</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Maroon" title="c4">s2</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Maroon" title="c4">s2</font> )</span><br/><span class="kw">thus </span><a NAME="E2:200_1_2_1_1"/>
( <font color="Maroon" title="c4">s2</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Maroon" title="c4">s2</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:200_1_2"><span class="lab"><font color="Green" title="E173">A2</font></span></a>, <a class="txt" href="#E1:200_1_2_1_1"><span class="lab"><font color="Green" title="E174">A3</font></span></a>, <a class="ref" href="group_9.html#T114" target="_self" title="GROUP_9:th.114">Th114</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">s2</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Maroon" title="c4">s2</font></span><br/><span class="kw">thus </span><a NAME="E3:200_1_2_1_1"/>
<font color="Maroon" title="c4">s2</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Maroon" title="c4">s2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#T113" target="_self" title="GROUP_9:th.113">Th113</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="200_1_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:200_1_2_1_2"/><span class="lab"><font color="Green" title="E174">A4</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">s2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">s19</font>, <font color="Olive" title="b2">s29</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font> st <br/>( <font color="Olive" title="b1">s19</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Olive" title="b2">s29</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Olive" title="b1">s19</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Olive" title="b2">s29</font> )</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c5">s29</font> = <font color="Maroon" title="c3">s1</font>;<br/><span class="kw">set </span><font color="Maroon" title="c6">s19</font> = <font color="Maroon" title="c3">s1</font>;<br/><span class="kw">take </span>
<font color="Maroon" title="c3">s1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">s29</font> being  <a href="group_9.html#NM5" title="GROUP_9:NM.5">CompositionSeries</a> of <font color="Maroon" title="c2">G</font> st <br/>( <font color="Maroon" title="c3">s1</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Olive" title="b1">s29</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Maroon" title="c3">s1</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Olive" title="b1">s29</font> )</span><br/><span class="kw">take </span>
<font color="Maroon" title="c3">s1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">s1</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Maroon" title="c3">s1</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Maroon" title="c3">s1</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Maroon" title="c3">s1</font> )</span><br/><span class="kw">thus </span><a NAME="E2:200_1_2_1_2"/>
( <font color="Maroon" title="c3">s1</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Maroon" title="c3">s1</font> <a href="group_9.html#R4" title="GROUP_9:pred.4">is_finer_than</a> <font color="Maroon" title="c4">s2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:200_1_2"><span class="lab"><font color="Green" title="E173">A2</font></span></a>, <a class="txt" href="#E1:200_1_2_1_2"><span class="lab"><font color="Green" title="E174">A4</font></span></a>, <a class="ref" href="group_9.html#T114" target="_self" title="GROUP_9:th.114">Th114</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">s1</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Maroon" title="c3">s1</font></span><br/><span class="kw">thus </span><a NAME="E3:200_1_2_1_2"/>
<font color="Maroon" title="c3">s1</font> <a href="group_9.html#R5" title="GROUP_9:pred.5">is_equivalent_with</a> <font color="Maroon" title="c3">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#T113" target="_self" title="GROUP_9:th.113">Th113</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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