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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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> holds  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V</font> is    <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of  <a href="rmod_2.html#K2" title="RMOD_2:func.2">(Omega).</a> <font color="Olive" title="b1">V</font></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font> is    <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of  <a href="rmod_2.html#K2" title="RMOD_2:func.2">(Omega).</a> <font color="Maroon" title="c2">V</font></span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">v</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/>
<a NAME="E2:90"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</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="c2">V</font>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font> ;<br/>
<a NAME="E4:90"/>
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="rmod_2.html#K3" title="RMOD_2:func.3">+</a> <span class="p1">(<span class="default"><a href="rmod_2.html#K2" title="RMOD_2:func.2">(Omega).</a> <font color="Maroon" title="c2">V</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_2.html#T62" target="_self" title="RMOD_2:th.62">Th62</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:90"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font> is    <a href="rmod_2.html#M2" title="RMOD_2:mode.2">Coset</a> of  <a href="rmod_2.html#K2" title="RMOD_2:func.2">(Omega).</a> <font color="Maroon" title="c2">V</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_2.html#D6" target="_self" title="RMOD_2:def.6">Def6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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