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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="rmod_4.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:22_1_2"/><i><font color="Green">E11</font></i>: 
 <a href="rmod_4.html#K2" target="_self">Carrier</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E2:22_1_2"/><i><font color="Green">E12</font></i>: 
 <a href="rmod_4.html#K2" target="_self">Carrier</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/><div><i><font color="Green">E13</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_2_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:22_1_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">c<sub>2</sub></font> : <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 ;<br/><b>hence </b><a NAME="E3:22_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="rmod_4.html#E1:22_1_2"><i><font color="Green">E11</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:22_1_2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:22_1_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">c<sub>2</sub></font> : <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 ;<br/><b>hence </b><a NAME="E3:22_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="rmod_4.html#E2:22_1_2"><i><font color="Green">E12</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:22_1_2_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="rmod_4.html#E3:22_1_2_1"><i><font color="Green">E13</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:22_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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