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<div class="add">

<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c3">W1</font>, <font color="Maroon" title="c4">W2</font> be    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font>;<br/>







<b>set </b><font color="Maroon" title="c5">VW1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font>;<br/>
<b>set </b><font color="Maroon" title="c6">VW2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font>;<br/>
<b>thus </b><a NAME="E1:46"/>
( for <font color="Olive" title="b1">W</font> being   <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font>  holds not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font> or <font color="Maroon" title="c3">W1</font> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c4">W2</font> or <font color="Maroon" title="c4">W2</font> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c3">W1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c7">W</font> being    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font><b> such that </b><a NAME="E2:46_1"/><i><font color="Green" title="E33">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c8">VW</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">W</font>;<br/>
<b>assume </b><a NAME="E3:46_1"/>
( <font color="Maroon" title="c3">W1</font> is  not    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c4">W2</font> &amp; <font color="Maroon" title="c4">W2</font> is  not    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c3">W1</font> )
 ;<br/>

<a NAME="E4:46_1"/><b>then </b><i><font color="Green" title="E34">A2</font></i>: 
( not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font> <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 <font color="Maroon" title="c4">W2</font> &amp; not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font> <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 <font color="Maroon" title="c3">W1</font> )
 
<b>by </b><i><a class="ref" href="rmod_2.html#T35" title="RMOD_2:th.35">RMOD_2:35</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c9">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:46_1"/><i><font color="Green" title="E35">A3</font></i>: 
<font color="Maroon" title="c9">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 <font color="Maroon" title="c3">W1</font>
 <b>and </b><br/><a NAME="E7:46_1"/><i><font color="Green" title="E36">A4</font></i>: 
not <font color="Maroon" title="c9">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 <font color="Maroon" title="c4">W2</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E9:46_1"/><i><font color="Green" title="E37">A5</font></i>: 
<font color="Maroon" title="c10">y</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 <font color="Maroon" title="c4">W2</font>
 <b>and </b><br/><a NAME="E10:46_1"/><i><font color="Green" title="E38">A6</font></i>: 
not <font color="Maroon" title="c10">y</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 <font color="Maroon" title="c3">W1</font>
 <b>by </b><i><a class="txt" href="rmod_3.html#E4:46_1"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c9">x</font> as    <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="c3">W1</font> <b>by </b><i><a class="txt" href="rmod_3.html#E6:46_1"><i><font color="Green" title="E35">A3</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">x</font> = <font color="Maroon" title="c11">x</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="rmod_2.html#T18" title="RMOD_2:th.18">RMOD_2:18</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">y</font> = <font color="Maroon" title="c10">y</font> as    <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="c4">W2</font> <b>by </b><i><a class="txt" href="rmod_3.html#E9:46_1"><i><font color="Green" title="E37">A5</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c14">y</font> = <font color="Maroon" title="c13">y</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="rmod_2.html#T18" title="RMOD_2:th.18">RMOD_2:18</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">A1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">W</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="rmod_2.html#D2" title="RMOD_2:def.2">RMOD_2:def 2</a></i>;<br/>
<a NAME="E16:46_1"/>
( <font color="Maroon" title="c12">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 <font color="Maroon" title="c7">W</font> &amp; <font color="Maroon" title="c14">y</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 <font color="Maroon" title="c7">W</font> &amp; <font color="Maroon" title="c15">A1</font> is <a href="rmod_2.html#V1" title="RMOD_2:attr.1">linearly-closed</a> )
 
<b>by </b><i><a class="txt" href="rmod_3.html#E2:46_1"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="rmod_2.html#T41" title="RMOD_2:th.41">RMOD_2:41</a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E17:46_1"/><b>then </b><i><font color="Green" title="E39">A7</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c14">y</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 <font color="Maroon" title="c7">W</font>
 
<b>by </b><i><a class="ref" href="rmod_2.html#D1" title="RMOD_2:def.1">RMOD_2:def 1</a></i>;<br/>
<div><i><font color="Green" title="E40">A8</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:46_1_1"/><i><font color="Green" title="E41">A9</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c14">y</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 <font color="Maroon" title="c3">W1</font>
 ;<br/><b>reconsider </b><font color="Maroon" title="c16">A2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="rmod_2.html#D2" title="RMOD_2:def.2">RMOD_2:def 2</a></i>;<br/><a NAME="E3:46_1_1"/>
<font color="Maroon" title="c16">A2</font> is <a href="rmod_2.html#V1" title="RMOD_2:attr.1">linearly-closed</a>
 <b>by </b><i><a class="ref" href="rmod_2.html#T41" title="RMOD_2:th.41">RMOD_2:41</a></i>;<br/><a NAME="E4:46_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c14">y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c12">x</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c12">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 <font color="Maroon" title="c3">W1</font>
 <b>by </b><i><a class="txt" href="rmod_3.html#E1:46_1_1"><i><font color="Green" title="E41">A9</font></i></a>, <a class="ref" href="rmod_2.html#T6" title="RMOD_2:th.6">RMOD_2:6</a></i>;<br/><a NAME="E5:46_1_1"/><b>then </b>
<font color="Maroon" title="c14">y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">x</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c12">x</font></span>)</span> <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 <font color="Maroon" title="c3">W1</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>;<br/><a NAME="E6:46_1_1"/><b>then </b>
<font color="Maroon" title="c14">y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font></span>)</span> <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 <font color="Maroon" title="c3">W1</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T66" title="VECTSP_1:th.66">VECTSP_1:66</a></i>;<br/><b>hence </b><a NAME="E7:46_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="rmod_3.html#E10:46_1"><i><font color="Green" title="E38">A6</font></i></a>, <a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:46_1_2"/><i><font color="Green" title="E41">A10</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c14">y</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 <font color="Maroon" title="c4">W2</font>
 ;<br/><b>reconsider </b><font color="Maroon" title="c16">A2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="rmod_2.html#D2" title="RMOD_2:def.2">RMOD_2:def 2</a></i>;<br/><a NAME="E3:46_1_2"/>
<font color="Maroon" title="c16">A2</font> is <a href="rmod_2.html#V1" title="RMOD_2:attr.1">linearly-closed</a>
 <b>by </b><i><a class="ref" href="rmod_2.html#T41" title="RMOD_2:th.41">RMOD_2:41</a></i>;<br/><a NAME="E4:46_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c14">y</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c14">y</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 <font color="Maroon" title="c4">W2</font>
 <b>by </b><i><a class="txt" href="rmod_3.html#E1:46_1_2"><i><font color="Green" title="E41">A10</font></i></a>, <a class="ref" href="rmod_2.html#T6" title="RMOD_2:th.6">RMOD_2:6</a></i>;<br/><a NAME="E5:46_1_2"/><b>then </b>
<font color="Maroon" title="c12">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">y</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c14">y</font></span>)</span> <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 <font color="Maroon" title="c4">W2</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>;<br/><a NAME="E6:46_1_2"/><b>then </b>
<font color="Maroon" title="c12">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font></span>)</span> <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 <font color="Maroon" title="c4">W2</font>
 <b>by </b><i><a class="ref" href="vectsp_1.html#T66" title="VECTSP_1:th.66">VECTSP_1:66</a></i>;<br/><b>hence </b><a NAME="E7:46_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="rmod_3.html#E7:46_1"><i><font color="Green" title="E36">A4</font></i></a>, <a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E20:46_1"/>
contradiction
 <b>by </b><i><a class="txt" href="rmod_3.html#E2:46_1"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="rmod_3.html#E17:46_1"><i><font color="Green" title="E39">A7</font></i></a>, <a class="txt" href="rmod_3.html#E18:46_1"><i><font color="Green" title="E40">A8</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:46"/><i><font color="Green" title="E33">A11</font></i>: 
( <font color="Maroon" title="c3">W1</font> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c4">W2</font> or <font color="Maroon" title="c4">W2</font> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c3">W1</font> )
 ;<br/>

<div><i><font color="Green" title="E34">A12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:46_2"/>
<font color="Maroon" title="c3">W1</font> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c4">W2</font>
 ;<br/><a NAME="E2:46_2"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font> <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 <font color="Maroon" title="c4">W2</font>
 <b>by </b><i><a class="ref" href="rmod_2.html#D2" title="RMOD_2:def.2">RMOD_2:def 2</a></i>;<br/><a NAME="E3:46_2"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/><b>hence </b><a NAME="E4:46_2"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <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" title="b1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:46_3"/>
<font color="Maroon" title="c4">W2</font> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c3">W1</font>
 ;<br/><a NAME="E2:46_3"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font> <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 <font color="Maroon" title="c3">W1</font>
 <b>by </b><i><a class="ref" href="rmod_2.html#D2" title="RMOD_2:def.2">RMOD_2:def 2</a></i>;<br/><a NAME="E3:46_3"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/><b>hence </b><a NAME="E4:46_3"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <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" title="b1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:46"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <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" title="b1">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">W2</font>
 <b>by </b><i><a class="txt" href="rmod_3.html#E2:46"><i><font color="Green" title="E33">A11</font></i></a>, <a class="txt" href="rmod_3.html#E3:46"><i><font color="Green" title="E34">A12</font></i></a></i>;<br/>


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