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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V</font> being  <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b2">W1</font>, <font color="Olive" title="b3">W2</font> being <a href="vectsp_2.html#V2" title="VECTSP_2:attr.2">strict</a>  <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Olive" title="b1">V</font><br/> for <font color="Olive" title="b4">C1</font> being   <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of <font color="Olive" title="b2">W1</font><br/> for <font color="Olive" title="b5">C2</font> being   <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of <font color="Olive" title="b3">W2</font>  st <font color="Olive" title="b4">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">C2</font> holds <br/><font color="Olive" title="b2">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">W2</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W1</font>, <font color="Olive" title="b2">W2</font> being <a href="vectsp_2.html#V2" title="VECTSP_2:attr.2">strict</a>  <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font><br/> for <font color="Olive" title="b3">C1</font> being   <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of <font color="Olive" title="b1">W1</font><br/> for <font color="Olive" title="b4">C2</font> being   <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of <font color="Olive" title="b2">W2</font>  st <font color="Olive" title="b3">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">C2</font> holds <br/><font color="Olive" title="b1">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">W2</font></span><br/><b>let </b><font color="Maroon" title="c3">W1</font>, <font color="Maroon" title="c4">W2</font> be  <a href="vectsp_2.html#V2" title="VECTSP_2:attr.2">strict</a>  <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C1</font> being   <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of <font color="Maroon" title="c3">W1</font><br/> for <font color="Olive" title="b2">C2</font> being   <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of <font color="Maroon" title="c4">W2</font>  st <font color="Olive" title="b1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">C2</font> holds <br/><font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font></span><br/><b>let </b><font color="Maroon" title="c5">C1</font> be    <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of <font color="Maroon" title="c3">W1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C2</font> being   <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of <font color="Maroon" title="c4">W2</font>  st <font color="Maroon" title="c5">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">C2</font> holds <br/><font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font></span><br/><b>let </b><font color="Maroon" title="c6">C2</font> be    <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of <font color="Maroon" title="c4">W2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">C2</font> implies <font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font> )</span><br/>









<a NAME="E1:70"/><i><font color="Green" title="E47">A1</font></i>: 
 ex <font color="Olive" title="b1">v1</font> being  <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> st <font color="Maroon" title="c5">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v1</font> <a href="rmod_2.html#K3" title="RMOD_2:func.3">+</a> <font color="Maroon" title="c3">W1</font>
 
<b>by </b><i><a class="ref" href="rmod_2.html#D6" target="_self" title="RMOD_2:def.6">Def6</a></i>;<br/>
<a NAME="E2:70"/>
 ex <font color="Olive" title="b1">v2</font> being  <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> st <font color="Maroon" title="c6">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v2</font> <a href="rmod_2.html#K3" title="RMOD_2:func.3">+</a> <font color="Maroon" title="c4">W2</font>
 
<b>by </b><i><a class="ref" href="rmod_2.html#D6" target="_self" title="RMOD_2:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E3:70"/>
( <font color="Maroon" title="c5">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">C2</font> implies <font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font> )
 <b>by </b><i><a class="txt" href="#E1:70"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="rmod_2.html#T80" target="_self" title="RMOD_2:th.80">Th80</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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