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

<span class="kw">set </span><font color="Maroon" title="c4">X</font> = <span class="p1"> { <span class="default"> <font color="Olive" title="b1">l</font> where <font color="Olive" title="b1">l</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> : verum </span> } </span> ;<br/>
<a NAME="E1:42_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">l</font> where <font color="Olive" title="b1">l</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> : verum </span> } </span>  <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="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="42_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">l</font> where <font color="Olive" title="b1">l</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> : verum </span> } </span>  or <font color="Maroon" title="c5">x</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="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:42_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">l</font> where <font color="Olive" title="b1">l</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> : verum </span> } </span> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">x</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="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span></span><br/>

<a NAME="E2:42_1_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> st <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">l</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:42_1_1_1"/>
<font color="Maroon" title="c5">x</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="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul02.html#D29" target="_self" onmouseover="rs('zmodul02/D29')" onmouseout="rh()">Def29</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">X</font> = <span class="p1"> { <span class="default"> <font color="Olive" title="b1">l</font> where <font color="Olive" title="b1">l</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> : verum </span> } </span>  as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span> ;<br/>
<a NAME="E3:42_1_1"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
<font color="Maroon" title="c5">X</font> is  <a href="vectsp_4.html#V1" title="VECTSP_4:attr.1">linearly-closed</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="42_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">thus </span><a NAME="E1:42_1_1_2"/>
 for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">u</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <span class="p1">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>  st <font color="Olive" title="b1">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> &amp; <font color="Olive" title="b2">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> holds <br/><font color="Olive" title="b1">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font>
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="vectsp_4.html#D1" onmouseover="rs('vectsp_4/D1')" onmouseout="rh()">VECTSP_4:def 1</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font><br/>  for <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>2</sub></font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> or <font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive">b<sub>2</sub></font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="42_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">v</font>, <font color="Maroon" title="c7">u</font> be   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <span class="p1">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> &amp; <font color="Maroon" title="c7">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> implies <font color="Maroon" title="c6">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:42_1_1_2_1"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<font color="Maroon" title="c6">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font>
 <span class="kw">and </span><br/><a NAME="E2:42_1_1_2_1"/><span class="lab"><font color="Green" title="E23">A3</font></span>: 
<font color="Maroon" title="c7">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c8">l1</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font><span class="kw"> such that </span><br/><a NAME="E4:42_1_1_2_1"/><span class="lab"><font color="Green" title="E24">A4</font></span>: 
<font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">l1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1_1_2_1"><span class="lab"><font color="Green" title="E22">A2</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">l2</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font><span class="kw"> such that </span><br/><a NAME="E6:42_1_1_2_1"/><span class="lab"><font color="Green" title="E25">A5</font></span>: 
<font color="Maroon" title="c7">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">l2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_1_1_2_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a></span>;<br/>
<a NAME="E7:42_1_1_2_1"/><span class="lab"><font color="Green" title="E26">A6</font></span>: 
<font color="Maroon" title="c7">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p1">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c9">l2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:42_1_1_2_1"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="ref" href="rlvect_2.html#D1" onmouseover="rs('rlvect_2/D1')" onmouseout="rh()">RLVECT_2:def 1</a>, <a class="ref" href="rlvect_1.html#T1" onmouseover="rs('rlvect_1/T1')" onmouseout="rh()">RLVECT_1:1</a></span>;<br/>
<a NAME="E8:42_1_1_2_1"/>
<font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p1">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c8">l1</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1_2_1"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="ref" href="rlvect_2.html#D1" onmouseover="rs('rlvect_2/D1')" onmouseout="rh()">RLVECT_2:def 1</a>, <a class="ref" href="rlvect_1.html#T1" onmouseover="rs('rlvect_1/T1')" onmouseout="rh()">RLVECT_1:1</a></span>;<br/>
<a NAME="E9:42_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">l1</font> <a href="vectsp_6.html#K5" title="VECTSP_6:func.5">+</a> <font color="Maroon" title="c9">l2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:42_1_1_2_1"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="ref" href="zmodul02.html#T47" target="_self" onmouseover="rs('zmodul02/T47')" onmouseout="rh()">Th47</a></span>;<br/>
<a NAME="E10:42_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">u</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul02.html#T27" target="_self" onmouseover="rs('zmodul02/T27')" onmouseout="rh()">Th27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:42_1_1_2_1"/>
<font color="Maroon" title="c6">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>

<span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> or <font color="Maroon" title="c6">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">v</font> be   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <span class="p1">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> or <font color="Maroon" title="c6">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font> )</span><br/>



<span class="kw">assume </span><a NAME="E2:42_1_1_2"/>
<font color="Maroon" title="c7">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font><span class="kw"> such that </span><br/><a NAME="E4:42_1_1_2"/><span class="lab"><font color="Green" title="E22">A7</font></span>: 
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">l</font>
 ;<br/>
<font color="Maroon" title="c6">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">v</font> = 
<font color="Maroon" title="c6">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> (<span class="p2">(<span class="default"><a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font></span>)</span>,<font color="Maroon" title="c8">l</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1_1_2"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="ref" href="rlvect_2.html#D1" onmouseover="rs('rlvect_2/D1')" onmouseout="rh()">RLVECT_2:def 1</a>, <a class="ref" href="rlvect_1.html#T1" onmouseover="rs('rlvect_1/T1')" onmouseout="rh()">RLVECT_1:1</a></span>
<br/>.= 
<font color="Maroon" title="c6">a</font> <a href="vectsp_6.html#K6" title="VECTSP_6:func.6">*</a> <font color="Maroon" title="c8">l</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul02.html#T48" target="_self" onmouseover="rs('zmodul02/T48')" onmouseout="rh()">Th48</a></span>
;<br/>
<a NAME="E6:42_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">v</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul02.html#T31" target="_self" onmouseover="rs('zmodul02/T31')" onmouseout="rh()">Th31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:42_1_1_2"/>
<font color="Maroon" title="c6">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="E4:42_1_1"/>
 <a href="vectsp_6.html#K2" title="VECTSP_6:func.2">ZeroLC</a> <font color="Maroon" title="c2">V</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul02.html#T11" target="_self" onmouseover="rs('zmodul02/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E5:42_1_1"/><span class="kw">then </span>
 <a href="vectsp_6.html#K2" title="VECTSP_6:func.2">ZeroLC</a> <font color="Maroon" title="c2">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">X</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E6:42_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of  <a href="zmodul02.html#K16" title="ZMODUL02:func.16">LC_Z_Module</a> <font color="Maroon" title="c2">V</font> st  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">l</font> where <font color="Olive" title="b2">l</font> is    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> : verum </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42_1_1"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="zmodul01.html#T50" onmouseover="rs('zmodul01/T50')" onmouseout="rh()">ZMODUL01:50</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
