<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</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">W1</font>, <font color="Olive" title="b2">W2</font> being   <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b3">C1</font> being   <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Olive" title="b1">W1</font><br/> for <font color="Olive" title="b4">C2</font> being   <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Olive" title="b2">W2</font>  st <font color="Olive" title="b3">C1</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Olive" title="b4">C2</font> holds <br/><font color="Olive" title="b3">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b4">C2</font> is    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Olive" title="b1">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Olive" title="b2">W2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">W1</font>, <font color="Maroon" title="c3">W2</font> be    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</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">C1</font> being   <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c2">W1</font><br/> for <font color="Olive" title="b2">C2</font> being   <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c3">W2</font>  st <font color="Olive" title="b1">C1</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Olive" title="b2">C2</font> holds <br/><font color="Olive" title="b1">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">C2</font> is    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">C1</font> be    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c2">W1</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">C2</font> being   <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c3">W2</font>  st <font color="Maroon" title="c4">C1</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Olive" title="b1">C2</font> holds <br/><font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b1">C2</font> is    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">C2</font> be    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c3">W2</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">C1</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c5">C2</font> implies <font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font> is    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font> )</span><br/>









<span class="kw">consider </span><font color="Maroon" title="c6">v</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">C</font> = <font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font>;<br/>
<span class="kw">assume </span><a NAME="E2:59"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a> <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">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font> is    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">v</font> = <font color="Maroon" title="c6">v</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<a NAME="E4:59"/>
<font color="Maroon" title="c8">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E5:59"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<font color="Maroon" title="c5">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c3">W2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlsub_1.html#T94" title="RLSUB_1:th.94">RLSUB_1:94</a></span>;<br/>
<a NAME="E6:59"/>
<font color="Maroon" title="c8">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E7:59"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A3</font></span>: 
<font color="Maroon" title="c4">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c2">W1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlsub_1.html#T94" title="RLSUB_1:th.94">RLSUB_1:94</a></span>;<br/>
<a NAME="E8:59"/>
<font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font> is    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">take </span>
<font color="Maroon" title="c8">v</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="rlsub_1.html#D6" title="RLSUB_1:def.6">RLSUB_1:def 6</a> <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">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span>)</span></span><br/>

<span class="kw">thus </span><a NAME="E1:59_1"/>
<font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span>)</span>
  <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <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="c8">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:59_1_1"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</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="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span>)</span></span><br/>

<a NAME="E2:59_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">u1</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E4:59_1_1"/><span class="lab"><font color="Green" title="E46">A5</font></span>: 
<font color="Maroon" title="c10">u1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">W1</font>
 <span class="kw">and </span><br/><a NAME="E5:59_1_1"/><span class="lab"><font color="Green" title="E47">A6</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c10">u1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:59"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="rlsub_1.html#T79" title="RLSUB_1:th.79">RLSUB_1:79</a></span>;<br/>
<a NAME="E6:59_1_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59_1_1"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">u2</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E8:59_1_1"/><span class="lab"><font color="Green" title="E48">A7</font></span>: 
<font color="Maroon" title="c11">u2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">W2</font>
 <span class="kw">and </span><br/><a NAME="E9:59_1_1"/><span class="lab"><font color="Green" title="E49">A8</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c11">u2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:59"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="rlsub_1.html#T79" title="RLSUB_1:th.79">RLSUB_1:79</a></span>;<br/>
<a NAME="E10:59_1_1"/>
<font color="Maroon" title="c10">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">u2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:59_1_1"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="txt" href="#E9:59_1_1"><span class="lab"><font color="Green" title="E49">A8</font></span></a>, <a class="ref" href="rlvect_1.html#T21" title="RLVECT_1:th.21">RLVECT_1:21</a></span>;<br/>
<a NAME="E11:59_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">u1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:59_1_1"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="txt" href="#E8:59_1_1"><span class="lab"><font color="Green" title="E48">A7</font></span></a>, <a class="ref" href="rlsub_2.html#T7" target="_self" title="RLSUB_2:th.7">Th7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:59_1_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:59_1_1"><span class="lab"><font color="Green" title="E47">A6</font></span></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>

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span>)</span> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:59_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span>)</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="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">u</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E4:59_1"/><span class="lab"><font color="Green" title="E45">A9</font></span>: 
<font color="Maroon" title="c10">u</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font>
 <span class="kw">and </span><br/><a NAME="E5:59_1"/><span class="lab"><font color="Green" title="E46">A10</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c10">u</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlsub_1.html#T79" title="RLSUB_1:th.79">RLSUB_1:79</a></span>;<br/>
<a NAME="E6:59_1"/>
<font color="Maroon" title="c10">u</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">W2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:59_1"><span class="lab"><font color="Green" title="E45">A9</font></span></a>, <a class="ref" href="rlsub_2.html#T7" target="_self" title="RLSUB_2:th.7">Th7</a></span>;<br/>
<a NAME="E7:59_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A11</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c8">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b1">u2</font></span>)</span> where <font color="Olive" title="b1">u2</font> is   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> : <font color="Olive" title="b1">u2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">W2</font> </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:59_1"><span class="lab"><font color="Green" title="E46">A10</font></span></a></span>;<br/>
<a NAME="E8:59_1"/>
<font color="Maroon" title="c10">u</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">W1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:59_1"><span class="lab"><font color="Green" title="E45">A9</font></span></a>, <a class="ref" href="rlsub_2.html#T7" target="_self" title="RLSUB_2:th.7">Th7</a></span>;<br/>
<a NAME="E9:59_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c8">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b1">u1</font></span>)</span> where <font color="Olive" title="b1">u1</font> is   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> : <font color="Olive" title="b1">u1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">W1</font> </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:59_1"><span class="lab"><font color="Green" title="E46">A10</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:59_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:59"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="txt" href="#E5:59"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E7:59_1"><span class="lab"><font color="Green" title="E47">A11</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</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>
<span class="kw">hence </span><a NAME="E9:59"/>
<font color="Maroon" title="c4">C1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">C2</font> is    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font>
 ; <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>
