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<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">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>thus </b><a NAME="E1:21"/>
for <font color="Olive" title="b1">W1</font> being <a href="vectsp_2.html#V3" title="VECTSP_2:attr.3">strict</a>  <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">W1</font> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c3">W2</font> holds <br/><font color="Olive" title="b1">W1</font> <a href="rmod_3.html#K2" title="RMOD_3:func.2">/\</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">W1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">W1</font> be  <a href="vectsp_2.html#V3" title="VECTSP_2:attr.3">strict</a>  <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font>;<br/>

<b>assume </b><a NAME="E1:21_1"/>
<font color="Maroon" title="c4">W1</font> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c3">W2</font>
 ;<br/>

<a NAME="E2:21_1"/><b>then </b><i><font color="Green" title="E20">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">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="c3">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="E3:21_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">W1</font> <a href="rmod_3.html#K2" title="RMOD_3:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span>)</span> <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">W1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">W2</font>
 
<b>by </b><i><a class="ref" href="rmod_3.html#D2" target="_self" title="RMOD_3:def.2">Def2</a></i>;<br/>
<a NAME="E4:21_1"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">W1</font> <a href="rmod_3.html#K2" title="RMOD_3:func.2">/\</a> <font color="Maroon" title="c3">W2</font></span>)</span> <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">W1</font>
 
<b>by </b><i><a class="txt" href="rmod_3.html#E2:21_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>;<br/>
<b>hence </b><a NAME="E5:21_1"/>
<font color="Maroon" title="c4">W1</font> <a href="rmod_3.html#K2" title="RMOD_3:func.2">/\</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W1</font>
 <b>by </b><i><a class="ref" href="rmod_2.html#T37" title="RMOD_2:th.37">RMOD_2:37</a></i>;<br/>


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

<b>thus </b><a NAME="E2:21"/>
for <font color="Olive" title="b1">W1</font> being   <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">W1</font> <a href="rmod_3.html#K2" title="RMOD_3:func.2">/\</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">W1</font> holds <br/><font color="Olive" title="b1">W1</font> is    <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c3">W2</font>
 <b>by </b><i><a class="ref" href="rmod_3.html#T20" target="_self" title="RMOD_3:th.20">Th20</a></i>;<br/>


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